Dataset Viewer
data_source
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value | prompt
listlengths 1
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images listlengths 1
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| reward_model
dict | extra_info
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|---|---|---|---|---|
scibench_multimodal
|
[
{
"content": "<image>The graph of a function $f$ is given. State the value of $f(1)$.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
{
"gt_answer": "3",
"id": "scibench_multimodal--0",
"mc_options": null,
"original_question": "<image>The graph of a function $f$ is given. State the value of $f(1)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph shows the power consumption for a day in September in San Francisco. $P$ is measured in megawatts; $t$ is measured in hours starting at midnight. What was the power consumption at 6 AM?",
"role": "user"
}
] |
{
"ground_truth": "500 MW",
"style": "rule"
}
|
{
"gt_answer": "500 MW",
"id": "scibench_multimodal--1",
"mc_options": null,
"original_question": "<image>The graph shows the power consumption for a day in September in San Francisco. $P$ is measured in megawatts; $t$ is measured in hours starting at midnight. What was the power consumption at 6 AM?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 0^{+}} g(t)$.",
"role": "user"
}
] |
{
"ground_truth": "-2",
"style": "rule"
}
|
{
"gt_answer": "-2",
"id": "scibench_multimodal--2",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 0^{+}} g(t)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure 23-46a shows three plastic sheets that are large, parallel, and uniformly charged. Figure 23-46b gives the component of the net electric field along an $x$ axis through the sheets. The scale of the vertical axis is set by $E_s=6.0 \\times 10^5 \\mathrm{~N} / \\mathrm{C}$. What is the ratio of the charge density on sheet 3 to that on sheet 2 ?",
"role": "user"
}
] |
{
"ground_truth": "$-1.5$",
"style": "rule"
}
|
{
"gt_answer": "$-1.5$",
"id": "scibench_multimodal--3",
"mc_options": null,
"original_question": "<image>Figure 23-46a shows three plastic sheets that are large, parallel, and uniformly charged. Figure 23-46b gives the component of the net electric field along an $x$ axis through the sheets. The scale of the vertical axis is set by $E_s=6.0 \\times 10^5 \\mathrm{~N} / \\mathrm{C}$. What is the ratio of the charge density on sheet 3 to that on sheet 2 ?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Fig. 21-25, the particles have charges $q_1=-q_2=100 \\mathrm{nC}$ and $q_3=-q_4=200 \\mathrm{nC}$, and distance $a=$ $5.0 \\mathrm{~cm}$. What is the $x$ component of the net electrostatic force on particle 3?",
"role": "user"
}
] |
{
"ground_truth": "0.17 $\\mathrm{~N}$",
"style": "rule"
}
|
{
"gt_answer": "0.17 $\\mathrm{~N}$",
"id": "scibench_multimodal--4",
"mc_options": null,
"original_question": "<image>In Fig. 21-25, the particles have charges $q_1=-q_2=100 \\mathrm{nC}$ and $q_3=-q_4=200 \\mathrm{nC}$, and distance $a=$ $5.0 \\mathrm{~cm}$. What is the $x$ component of the net electrostatic force on particle 3?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Suppose you design an apparatus in which a uniformly charged disk of radius $R$ is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point $P$ at distance $2.00 R$ from the disk (Fig. 22-57a). Cost analysis suggests that you switch to a ring of the same outer radius $R$ but with inner radius $R / 2.00$ (Fig. 22-57b). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what percentage will you decrease the electric field magnitude at $P$ ?\r\n",
"role": "user"
}
] |
{
"ground_truth": "$28$ $\\%$",
"style": "rule"
}
|
{
"gt_answer": "$28$ $\\%$",
"id": "scibench_multimodal--5",
"mc_options": null,
"original_question": "<image>Suppose you design an apparatus in which a uniformly charged disk of radius $R$ is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point $P$ at distance $2.00 R$ from the disk (Fig. 22-57a). Cost analysis suggests that you switch to a ring of the same outer radius $R$ but with inner radius $R / 2.00$ (Fig. 22-57b). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what percentage will you decrease the electric field magnitude at $P$ ?\r\n"
}
|
|
scibench_multimodal
|
[
{
"content": "<image> The square surface shown in Fig. 23-30 measures $3.2 \\mathrm{~mm}$ on each side. It is immersed in a uniform electric field with magnitude $E=1800 \\mathrm{~N} / \\mathrm{C}$ and with field lines at an angle of $\\theta=35^{\\circ}$ with a normal to the surface, as shown. Take that normal to be directed \"outward,\" as though the surface were one face of a box. Calculate the electric flux through the surface.",
"role": "user"
}
] |
{
"ground_truth": "$-0.015$ $\\mathrm{~N} \\cdot \\mathrm{m}^2 / \\mathrm{C}$",
"style": "rule"
}
|
{
"gt_answer": "$-0.015$ $\\mathrm{~N} \\cdot \\mathrm{m}^2 / \\mathrm{C}$",
"id": "scibench_multimodal--6",
"mc_options": null,
"original_question": "<image> The square surface shown in Fig. 23-30 measures $3.2 \\mathrm{~mm}$ on each side. It is immersed in a uniform electric field with magnitude $E=1800 \\mathrm{~N} / \\mathrm{C}$ and with field lines at an angle of $\\theta=35^{\\circ}$ with a normal to the surface, as shown. Take that normal to be directed \"outward,\" as though the surface were one face of a box. Calculate the electric flux through the surface."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In crystals of the salt cesium chloride, cesium ions $\\mathrm{Cs}^{+}$form the eight corners of a cube and a chlorine ion $\\mathrm{Cl}^{-}$is at the cube's center (Fig. 21-36). The edge length of the cube is $0.40 \\mathrm{~nm}$. The $\\mathrm{Cs}^{+}$ions are each deficient by one electron (and thus each has a charge of $+e$ ), and the $\\mathrm{Cl}^{-}$ion has one excess electron (and thus has a charge of $-e$ ). What is the magnitude of the net electrostatic force exerted on the $\\mathrm{Cl}^{-}$ion by the eight $\\mathrm{Cs}^{+}$ions at the corners of the cube?",
"role": "user"
}
] |
{
"ground_truth": "$0$",
"style": "rule"
}
|
{
"gt_answer": "$0$",
"id": "scibench_multimodal--7",
"mc_options": null,
"original_question": "<image>In crystals of the salt cesium chloride, cesium ions $\\mathrm{Cs}^{+}$form the eight corners of a cube and a chlorine ion $\\mathrm{Cl}^{-}$is at the cube's center (Fig. 21-36). The edge length of the cube is $0.40 \\mathrm{~nm}$. The $\\mathrm{Cs}^{+}$ions are each deficient by one electron (and thus each has a charge of $+e$ ), and the $\\mathrm{Cl}^{-}$ion has one excess electron (and thus has a charge of $-e$ ). What is the magnitude of the net electrostatic force exerted on the $\\mathrm{Cl}^{-}$ion by the eight $\\mathrm{Cs}^{+}$ions at the corners of the cube?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Find the y coordinate of the center of mass of a uniform wire that subtends an arc $\\theta$ if the radius of the circular arc is $a$, as shown in Figure 9-A.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
{
"gt_answer": "0",
"id": "scibench_multimodal--8",
"mc_options": null,
"original_question": "<image>Find the y coordinate of the center of mass of a uniform wire that subtends an arc $\\theta$ if the radius of the circular arc is $a$, as shown in Figure 9-A."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A common test for AIDS is called the ELISA (enzyme-linked immunosorbent assay) test. Among 1 million people who are given the ELISA test, we can expect results similar to those given in the following table.\r\nIf one of these 1 million people is selected randomly, find the following probability of $P\\left(B_1\\right)$\r\n",
"role": "user"
}
] |
{
"ground_truth": "$\\frac{5000}{1000000}$",
"style": "rule"
}
|
{
"gt_answer": "$\\frac{5000}{1000000}$",
"id": "scibench_multimodal--9",
"mc_options": null,
"original_question": "<image>A common test for AIDS is called the ELISA (enzyme-linked immunosorbent assay) test. Among 1 million people who are given the ELISA test, we can expect results similar to those given in the following table.\r\nIf one of these 1 million people is selected randomly, find the following probability of $P\\left(B_1\\right)$\r\n"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Fig. 22-66, particle 1 (of charge $+1.00 \\mu \\mathrm{C}$ ), particle 2 (of charge $+1.00 \\mu \\mathrm{C})$, and particle 3 (of charge $Q$ ) form an equilateral triangle of edge length $a$. For what value of $Q$ (both sign and magnitude) does the net electric field produced by the particles at the center of the triangle vanish?",
"role": "user"
}
] |
{
"ground_truth": "$1.00$ $\\mu \\mathrm{C}$",
"style": "rule"
}
|
{
"gt_answer": "$1.00$ $\\mu \\mathrm{C}$",
"id": "scibench_multimodal--10",
"mc_options": null,
"original_question": "<image>In Fig. 22-66, particle 1 (of charge $+1.00 \\mu \\mathrm{C}$ ), particle 2 (of charge $+1.00 \\mu \\mathrm{C})$, and particle 3 (of charge $Q$ ) form an equilateral triangle of edge length $a$. For what value of $Q$ (both sign and magnitude) does the net electric field produced by the particles at the center of the triangle vanish?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Fig. 22-54, Figure 22-53 Problem 30. a nonconducting rod of length $L=$ $8.15 \\mathrm{~cm}$ has a charge $-q=-4.23 \\mathrm{fC}$ uniformly distributed along its length. What is the linear charge density of the rod? ",
"role": "user"
}
] |
{
"ground_truth": "$-5.19$ $10^{-14} \\mathrm{C} / \\mathrm{m}$",
"style": "rule"
}
|
{
"gt_answer": "$-5.19$ $10^{-14} \\mathrm{C} / \\mathrm{m}$",
"id": "scibench_multimodal--11",
"mc_options": null,
"original_question": "<image>In Fig. 22-54, Figure 22-53 Problem 30. a nonconducting rod of length $L=$ $8.15 \\mathrm{~cm}$ has a charge $-q=-4.23 \\mathrm{fC}$ uniformly distributed along its length. What is the linear charge density of the rod? "
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A bicycle pedal is pushed by a foot with a $60-\\mathrm{N}$ force as shown. The shaft of the pedal is $18 \\mathrm{~cm}$ long. Find the magnitude of the torque about $P$.\r\n",
"role": "user"
}
] |
{
"ground_truth": "$10.8\\sin(80^{\\circ})$ $\\mathrm{N}\\cdot \\mathrm{m}$",
"style": "rule"
}
|
{
"gt_answer": "$10.8\\sin(80^{\\circ})$ $\\mathrm{N}\\cdot \\mathrm{m}$",
"id": "scibench_multimodal--12",
"mc_options": null,
"original_question": "<image>A bicycle pedal is pushed by a foot with a $60-\\mathrm{N}$ force as shown. The shaft of the pedal is $18 \\mathrm{~cm}$ long. Find the magnitude of the torque about $P$.\r\n"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 2^{-}} g(t)$.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
{
"gt_answer": "2",
"id": "scibench_multimodal--13",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 2^{-}} g(t)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>$\\bullet \\bullet 17$ Two charged beads are on the plastic ring in Fig. 22-44a. Bead 2 , which is not shown, is fixed in place on the ring, which has radius $R=60.0 \\mathrm{~cm}$. Bead 1 , which is not fixed in place, is initially on the $x$ axis at angle $\\theta=0^{\\circ}$. It is then moved to the opposite side, at angle $\\theta=180^{\\circ}$, through the first and second quadrants of the $x y$ coordinate system. Figure 22-44b gives the $x$ component of the net electric field produced at the origin by the two beads as a function of $\\theta$, and Fig. 22-44c gives the $y$ component of that net electric field. The vertical axis scales are set by $E_{x s}=5.0 \\times 10^4 \\mathrm{~N} / \\mathrm{C}$ and $E_{y s}=$ $-9.0 \\times 10^4 \\mathrm{~N} / \\mathrm{C}$. At what angle $\\theta$ is bead 2 located?",
"role": "user"
}
] |
{
"ground_truth": "$-90$ $^{\\circ}$",
"style": "rule"
}
|
{
"gt_answer": "$-90$ $^{\\circ}$",
"id": "scibench_multimodal--14",
"mc_options": null,
"original_question": "<image>$\\bullet \\bullet 17$ Two charged beads are on the plastic ring in Fig. 22-44a. Bead 2 , which is not shown, is fixed in place on the ring, which has radius $R=60.0 \\mathrm{~cm}$. Bead 1 , which is not fixed in place, is initially on the $x$ axis at angle $\\theta=0^{\\circ}$. It is then moved to the opposite side, at angle $\\theta=180^{\\circ}$, through the first and second quadrants of the $x y$ coordinate system. Figure 22-44b gives the $x$ component of the net electric field produced at the origin by the two beads as a function of $\\theta$, and Fig. 22-44c gives the $y$ component of that net electric field. The vertical axis scales are set by $E_{x s}=5.0 \\times 10^4 \\mathrm{~N} / \\mathrm{C}$ and $E_{y s}=$ $-9.0 \\times 10^4 \\mathrm{~N} / \\mathrm{C}$. At what angle $\\theta$ is bead 2 located?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The cube in Fig. 23-31 has edge length $1.40 \\mathrm{~m}$ and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field, in newtons per coulomb, is given by $6.00 \\hat{\\mathrm{i}}$?",
"role": "user"
}
] |
{
"ground_truth": "$0$",
"style": "rule"
}
|
{
"gt_answer": "$0$",
"id": "scibench_multimodal--15",
"mc_options": null,
"original_question": "<image>The cube in Fig. 23-31 has edge length $1.40 \\mathrm{~m}$ and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field, in newtons per coulomb, is given by $6.00 \\hat{\\mathrm{i}}$?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Fig. 23-54, a solid sphere of radius $a=2.00 \\mathrm{~cm}$ is concentric with a spherical conducting shell of inner radius $b=2.00 a$ and outer radius $c=$ $2.40 a$. The sphere has a net uniform charge $q_1=+5.00 \\mathrm{fC}$; the shell has a net charge $q_2=-q_1$. What is the magnitude of the electric field at radial distance $r=0$?",
"role": "user"
}
] |
{
"ground_truth": "$0$",
"style": "rule"
}
|
{
"gt_answer": "$0$",
"id": "scibench_multimodal--16",
"mc_options": null,
"original_question": "<image>In Fig. 23-54, a solid sphere of radius $a=2.00 \\mathrm{~cm}$ is concentric with a spherical conducting shell of inner radius $b=2.00 a$ and outer radius $c=$ $2.40 a$. The sphere has a net uniform charge $q_1=+5.00 \\mathrm{fC}$; the shell has a net charge $q_2=-q_1$. What is the magnitude of the electric field at radial distance $r=0$?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>What is the y coordinate of the center of mass of the isosceles right triangle of uniform areal density shown in Figure 9-C?",
"role": "user"
}
] |
{
"ground_truth": "$\\frac{1}{3 \\sqrt{2}}$ $a$",
"style": "rule"
}
|
{
"gt_answer": "$\\frac{1}{3 \\sqrt{2}}$ $a$",
"id": "scibench_multimodal--17",
"mc_options": null,
"original_question": "<image>What is the y coordinate of the center of mass of the isosceles right triangle of uniform areal density shown in Figure 9-C?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure 22-52a shows a nonconducting rod with a uniformly distributed charge $+Q$. The rod forms a half-circle with radius $R$ and produces an electric field of magnitude $E_{\\mathrm{arc}}$ at its center of curvature $P$. If the arc is collapsed to a point at distance $R$ from $P$ (Fig. 22-52b), by what factor is the magnitude of the electric field at $P$ multiplied?",
"role": "user"
}
] |
{
"ground_truth": "$1.57$",
"style": "rule"
}
|
{
"gt_answer": "$1.57$",
"id": "scibench_multimodal--18",
"mc_options": null,
"original_question": "<image>Figure 22-52a shows a nonconducting rod with a uniformly distributed charge $+Q$. The rod forms a half-circle with radius $R$ and produces an electric field of magnitude $E_{\\mathrm{arc}}$ at its center of curvature $P$. If the arc is collapsed to a point at distance $R$ from $P$ (Fig. 22-52b), by what factor is the magnitude of the electric field at $P$ multiplied?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Two large parallel copper plates are $5.0 \\mathrm{~cm}$ apart and have a uniform electric field between them as depicted in Fig. 22-60. An electron is released from the negative plate at the same time that a proton is released from the positive plate. Neglect the force of the particles on each other and find their distance from the positive plate when they pass each other. ",
"role": "user"
}
] |
{
"ground_truth": "$27$ $\\mu \\mathrm{m}$",
"style": "rule"
}
|
{
"gt_answer": "$27$ $\\mu \\mathrm{m}$",
"id": "scibench_multimodal--19",
"mc_options": null,
"original_question": "<image>Two large parallel copper plates are $5.0 \\mathrm{~cm}$ apart and have a uniform electric field between them as depicted in Fig. 22-60. An electron is released from the negative plate at the same time that a proton is released from the positive plate. Neglect the force of the particles on each other and find their distance from the positive plate when they pass each other. "
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure 22-40 shows a proton (p) on the central axis through a disk with a uniform charge density due to excess electrons. The disk is seen from an edge-on view. Three of those electrons are shown: electron $\\mathrm{e}_c$ at the disk center and electrons $\\mathrm{e}_s$ at opposite sides of the disk, at radius $R$ from the center. The proton is initially at distance $z=R=2.00 \\mathrm{~cm}$ from the disk. At that location, what is the magnitude of the electric field $\\vec{E}_c$ due to electron $\\mathrm{e}_c$?",
"role": "user"
}
] |
{
"ground_truth": "$3.60$ $10^{-6} \\mathrm{~N} / \\mathrm{C}$",
"style": "rule"
}
|
{
"gt_answer": "$3.60$ $10^{-6} \\mathrm{~N} / \\mathrm{C}$",
"id": "scibench_multimodal--20",
"mc_options": null,
"original_question": "<image>Figure 22-40 shows a proton (p) on the central axis through a disk with a uniform charge density due to excess electrons. The disk is seen from an edge-on view. Three of those electrons are shown: electron $\\mathrm{e}_c$ at the disk center and electrons $\\mathrm{e}_s$ at opposite sides of the disk, at radius $R$ from the center. The proton is initially at distance $z=R=2.00 \\mathrm{~cm}$ from the disk. At that location, what is the magnitude of the electric field $\\vec{E}_c$ due to electron $\\mathrm{e}_c$?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image> In Fig. 22-64a, a particle of charge $+Q$ produces an electric field of magnitude $E_{\\text {part }}$ at point $P$, at distance $R$ from the particle. In Fig. 22-64b, that same amount of charge is spread uniformly along a circular arc that has radius $R$ and subtends an angle $\\theta$. The charge on the arc produces an electric field of magnitude $E_{\\mathrm{arc}}$ at its center of curvature $P$. For what value of $\\theta$ does $E_{\\text {arc }}=$ $0.500 E_{\\text {part }}$ ? (Hint: You will probably resort to a graphical solution.)",
"role": "user"
}
] |
{
"ground_truth": "$217$ $^{\\circ}$",
"style": "rule"
}
|
{
"gt_answer": "$217$ $^{\\circ}$",
"id": "scibench_multimodal--21",
"mc_options": null,
"original_question": "<image> In Fig. 22-64a, a particle of charge $+Q$ produces an electric field of magnitude $E_{\\text {part }}$ at point $P$, at distance $R$ from the particle. In Fig. 22-64b, that same amount of charge is spread uniformly along a circular arc that has radius $R$ and subtends an angle $\\theta$. The charge on the arc produces an electric field of magnitude $E_{\\mathrm{arc}}$ at its center of curvature $P$. For what value of $\\theta$ does $E_{\\text {arc }}=$ $0.500 E_{\\text {part }}$ ? (Hint: You will probably resort to a graphical solution.)"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Fig. 22-42, the three particles are fixed in place and have charges $q_1=q_2=$ $+e$ and $q_3=+2 e$. Distance $a=6.00 \\mu \\mathrm{m}$. What is the magnitude of the net electric field at point $P$ due to the particles?",
"role": "user"
}
] |
{
"ground_truth": "$160$ $\\mathrm{~N} / \\mathrm{C}$",
"style": "rule"
}
|
{
"gt_answer": "$160$ $\\mathrm{~N} / \\mathrm{C}$",
"id": "scibench_multimodal--22",
"mc_options": null,
"original_question": "<image>In Fig. 22-42, the three particles are fixed in place and have charges $q_1=q_2=$ $+e$ and $q_3=+2 e$. Distance $a=6.00 \\mu \\mathrm{m}$. What is the magnitude of the net electric field at point $P$ due to the particles?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Fig. 21-38, particle 1 of charge $+4 e$ is above a floor by distance $d_1=2.00 \\mathrm{~mm}$ and particle 2 of charge $+6 e$ is on the floor, at distance $d_2=6.00 \\mathrm{~mm}$ horizontally from particle 1 . What is the $x$ component of the electrostatic force on particle 2 due to particle $1 ?$",
"role": "user"
}
] |
{
"ground_truth": "$1.31$ $10^{-22} \\mathrm{~N}$",
"style": "rule"
}
|
{
"gt_answer": "$1.31$ $10^{-22} \\mathrm{~N}$",
"id": "scibench_multimodal--23",
"mc_options": null,
"original_question": "<image>In Fig. 21-38, particle 1 of charge $+4 e$ is above a floor by distance $d_1=2.00 \\mathrm{~mm}$ and particle 2 of charge $+6 e$ is on the floor, at distance $d_2=6.00 \\mathrm{~mm}$ horizontally from particle 1 . What is the $x$ component of the electrostatic force on particle 2 due to particle $1 ?$"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 2} g(t)$.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
{
"gt_answer": "0",
"id": "scibench_multimodal--24",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 2} g(t)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A cross-section of an airplane wing is shown. Measurements of the thickness of the wing, in centimeters, at 20-centimeter intervals are 5.8, 20.3, 26.7, 29.0, 27.6, 27.3, 23.8, 20.5, 15.1, 8.7, and 2.8. Use the Midpoint Rule to estimate the area of the wing's cross-section.",
"role": "user"
}
] |
{
"ground_truth": "4232 $\\mathrm{cm}^2$",
"style": "rule"
}
|
{
"gt_answer": "4232 $\\mathrm{cm}^2$",
"id": "scibench_multimodal--25",
"mc_options": null,
"original_question": "<image>A cross-section of an airplane wing is shown. Measurements of the thickness of the wing, in centimeters, at 20-centimeter intervals are 5.8, 20.3, 26.7, 29.0, 27.6, 27.3, 23.8, 20.5, 15.1, 8.7, and 2.8. Use the Midpoint Rule to estimate the area of the wing's cross-section."
}
|
|
scibench_multimodal
|
[
{
"content": "<image> In Fig. 21-32, particles 1 and 2 of charge $q_1=q_2=+3.20 \\times 10^{-19} \\mathrm{C}$ are on a $y$ axis at distance $d=17.0 \\mathrm{~cm}$ from the origin. Particle 3 of charge $q_3=+6.40 \\times 10^{-19} \\mathrm{C}$ is moved gradually along the $x$ axis from $x=0$ to $x=$ $+5.0 \\mathrm{~m}$. At what values of $x$ will the magnitude of the electrostatic force on the third particle from the other two particles be minimum?\r\n",
"role": "user"
}
] |
{
"ground_truth": "$0$",
"style": "rule"
}
|
{
"gt_answer": "$0$",
"id": "scibench_multimodal--26",
"mc_options": null,
"original_question": "<image> In Fig. 21-32, particles 1 and 2 of charge $q_1=q_2=+3.20 \\times 10^{-19} \\mathrm{C}$ are on a $y$ axis at distance $d=17.0 \\mathrm{~cm}$ from the origin. Particle 3 of charge $q_3=+6.40 \\times 10^{-19} \\mathrm{C}$ is moved gradually along the $x$ axis from $x=0$ to $x=$ $+5.0 \\mathrm{~m}$. At what values of $x$ will the magnitude of the electrostatic force on the third particle from the other two particles be minimum?\r\n"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure 22-45 shows an electric dipole. What is the direction (relative to the positive direction of the $x$ axis) of the dipole's electric field at point $P$, located at distance $r \\gg d$ ?",
"role": "user"
}
] |
{
"ground_truth": "$-90$ $^{\\circ}$",
"style": "rule"
}
|
{
"gt_answer": "$-90$ $^{\\circ}$",
"id": "scibench_multimodal--27",
"mc_options": null,
"original_question": "<image>Figure 22-45 shows an electric dipole. What is the direction (relative to the positive direction of the $x$ axis) of the dipole's electric field at point $P$, located at distance $r \\gg d$ ?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>B.A. Bovenzi and G.A. Pearse, Jr. (J. Chem. Soc. Dalton Trans., 2793 (1997)) synthesized coordination compounds of the tridentate ligand pyridine-2,6-diamidoxime $\\left(7, \\mathrm{C}_7 \\mathrm{H}_9 \\mathrm{~N}_5 \\mathrm{O}_2\\right)$. The compound which they isolated from the reaction of the ligand with $\\mathrm{CuSO}_4(\\mathrm{aq})$ did not contain a $\\left[\\mathrm{Cu}\\left(\\mathrm{C}_7 \\mathrm{H}_9 \\mathrm{~N}_5 \\mathrm{O}_2\\right)_2\\right]^{2+}$ complex cation as expected. Instead, X-ray diffraction analysis revealed a linear polymer of formula $\\left[\\mathrm{Cu}\\left(\\mathrm{C}_7 \\mathrm{H}_9 \\mathrm{~N}_5 \\mathrm{O}_2\\right)\\left(\\mathrm{SO}_4\\right) \\cdot 2 \\mathrm{H}_2 \\mathrm{O}\\right]_n$, which features bridging sulfate groups. The unit cell was primitive monoclinic with $a=1.0427 \\mathrm{~nm}, b=0.8876 \\mathrm{~nm}, c=1.3777 \\mathrm{~nm}$, and $\\beta=93.254^{\\circ}$. The mass density of the crystals is $2.024 \\mathrm{~g} \\mathrm{~cm}^{-3}$. How many monomer units are there in the unit cell?",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
{
"gt_answer": "4",
"id": "scibench_multimodal--28",
"mc_options": null,
"original_question": "<image>B.A. Bovenzi and G.A. Pearse, Jr. (J. Chem. Soc. Dalton Trans., 2793 (1997)) synthesized coordination compounds of the tridentate ligand pyridine-2,6-diamidoxime $\\left(7, \\mathrm{C}_7 \\mathrm{H}_9 \\mathrm{~N}_5 \\mathrm{O}_2\\right)$. The compound which they isolated from the reaction of the ligand with $\\mathrm{CuSO}_4(\\mathrm{aq})$ did not contain a $\\left[\\mathrm{Cu}\\left(\\mathrm{C}_7 \\mathrm{H}_9 \\mathrm{~N}_5 \\mathrm{O}_2\\right)_2\\right]^{2+}$ complex cation as expected. Instead, X-ray diffraction analysis revealed a linear polymer of formula $\\left[\\mathrm{Cu}\\left(\\mathrm{C}_7 \\mathrm{H}_9 \\mathrm{~N}_5 \\mathrm{O}_2\\right)\\left(\\mathrm{SO}_4\\right) \\cdot 2 \\mathrm{H}_2 \\mathrm{O}\\right]_n$, which features bridging sulfate groups. The unit cell was primitive monoclinic with $a=1.0427 \\mathrm{~nm}, b=0.8876 \\mathrm{~nm}, c=1.3777 \\mathrm{~nm}$, and $\\beta=93.254^{\\circ}$. The mass density of the crystals is $2.024 \\mathrm{~g} \\mathrm{~cm}^{-3}$. How many monomer units are there in the unit cell?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>This problem is quite challenging in setting up but takes only a few lines of algebra to solve. We deal with not only uniformly circular motion but also a ramp. However, we will not need a tilted coordinate system as with other ramps. Instead we can take a freeze-frame of the motion and work with simply horizontal and vertical axes. As always in this chapter, the starting point will be to apply Newton's second law, but that will require us to identify the force component that is responsible for the uniform circular motion.\r\n\r\nCurved portions of highways are always banked (tilted) to prevent cars from sliding off the highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the highway is wet, however, the frictional force may be negligible, and banking is then essential. Figure represents a car of mass $m$ as it moves at a constant speed $v$ of $20 \\mathrm{~m} / \\mathrm{s}$ around a banked circular track of radius $R=190 \\mathrm{~m}$. (It is a normal car, rather than a race car, which means that any vertical force from the passing air is negligible.) If the frictional force from the track is negligible, what bank angle $\\theta$ prevents sliding?",
"role": "user"
}
] |
{
"ground_truth": "12 $^{\\circ}$",
"style": "rule"
}
|
{
"gt_answer": "12 $^{\\circ}$",
"id": "scibench_multimodal--29",
"mc_options": null,
"original_question": "<image>This problem is quite challenging in setting up but takes only a few lines of algebra to solve. We deal with not only uniformly circular motion but also a ramp. However, we will not need a tilted coordinate system as with other ramps. Instead we can take a freeze-frame of the motion and work with simply horizontal and vertical axes. As always in this chapter, the starting point will be to apply Newton's second law, but that will require us to identify the force component that is responsible for the uniform circular motion.\r\n\r\nCurved portions of highways are always banked (tilted) to prevent cars from sliding off the highway. When a highway is dry, the frictional force between the tires and the road surface may be enough to prevent sliding. When the highway is wet, however, the frictional force may be negligible, and banking is then essential. Figure represents a car of mass $m$ as it moves at a constant speed $v$ of $20 \\mathrm{~m} / \\mathrm{s}$ around a banked circular track of radius $R=190 \\mathrm{~m}$. (It is a normal car, rather than a race car, which means that any vertical force from the passing air is negligible.) If the frictional force from the track is negligible, what bank angle $\\theta$ prevents sliding?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure shows a water-slide ride in which a glider is shot by a spring along a water-drenched (frictionless) track that takes the glider from a horizontal section down to ground level. As the glider then moves along ground-level track, it is gradually brought to rest by friction. The total mass of the glider and its rider is $m=200 \\mathrm{~kg}$, the initial compression of the spring is $d=5.00 \\mathrm{~m}$, the spring constant is $k=3.20 \\times$ $10^3 \\mathrm{~N} / \\mathrm{m}$, the initial height is $h=35.0 \\mathrm{~m}$, and the coefficient of kinetic friction along the ground-level track is $\\mu_k=0.800$. Through what distance $L$ does the glider slide along the ground-level track until it stops?",
"role": "user"
}
] |
{
"ground_truth": "69.3 m",
"style": "rule"
}
|
{
"gt_answer": "69.3 m",
"id": "scibench_multimodal--30",
"mc_options": null,
"original_question": "<image>Figure shows a water-slide ride in which a glider is shot by a spring along a water-drenched (frictionless) track that takes the glider from a horizontal section down to ground level. As the glider then moves along ground-level track, it is gradually brought to rest by friction. The total mass of the glider and its rider is $m=200 \\mathrm{~kg}$, the initial compression of the spring is $d=5.00 \\mathrm{~m}$, the spring constant is $k=3.20 \\times$ $10^3 \\mathrm{~N} / \\mathrm{m}$, the initial height is $h=35.0 \\mathrm{~m}$, and the coefficient of kinetic friction along the ground-level track is $\\mu_k=0.800$. Through what distance $L$ does the glider slide along the ground-level track until it stops?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A uniform ball, of mass $M=6.00 \\mathrm{~kg}$ and radius $R$, rolls smoothly from rest down a ramp at angle $\\theta=30.0^{\\circ}$ (Figure).\r\nThe ball descends a vertical height $h=1.20 \\mathrm{~m}$ to reach the bottom of the ramp. What is its speed at the bottom?",
"role": "user"
}
] |
{
"ground_truth": "4.10 m/s",
"style": "rule"
}
|
{
"gt_answer": "4.10 m/s",
"id": "scibench_multimodal--31",
"mc_options": null,
"original_question": "<image>A uniform ball, of mass $M=6.00 \\mathrm{~kg}$ and radius $R$, rolls smoothly from rest down a ramp at angle $\\theta=30.0^{\\circ}$ (Figure).\r\nThe ball descends a vertical height $h=1.20 \\mathrm{~m}$ to reach the bottom of the ramp. What is its speed at the bottom?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The main lesson of this sample problem is this: It is perfectly all right to choose an easy path instead of a hard path. Figure shows a $2.0 \\mathrm{~kg}$ block of slippery cheese that slides along a frictionless track from point $a$ to point $b$. The cheese travels through a total distance of $2.0 \\mathrm{~m}$ along the track, and a net vertical distance of $0.80 \\mathrm{~m}$. How much work is done on the cheese by the gravitational force during the slide?",
"role": "user"
}
] |
{
"ground_truth": "15.7 J",
"style": "rule"
}
|
{
"gt_answer": "15.7 J",
"id": "scibench_multimodal--32",
"mc_options": null,
"original_question": "<image>The main lesson of this sample problem is this: It is perfectly all right to choose an easy path instead of a hard path. Figure shows a $2.0 \\mathrm{~kg}$ block of slippery cheese that slides along a frictionless track from point $a$ to point $b$. The cheese travels through a total distance of $2.0 \\mathrm{~m}$ along the track, and a net vertical distance of $0.80 \\mathrm{~m}$. How much work is done on the cheese by the gravitational force during the slide?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Figure, a cockroach with mass $m$ rides on a disk of mass $6.00 \\mathrm{~m}$ and radius $R$. The disk rotates like a merry-go-round around its central axis at angular speed $\\omega_i=1.50 \\mathrm{rad} / \\mathrm{s}$. The cockroach is initially at radius $r=0.800 R$, but then it crawls out to the rim of the disk. Treat the cockroach as a particle. What then is the angular speed?",
"role": "user"
}
] |
{
"ground_truth": "1.37 rad/s",
"style": "rule"
}
|
{
"gt_answer": "1.37 rad/s",
"id": "scibench_multimodal--33",
"mc_options": null,
"original_question": "<image>In Figure, a cockroach with mass $m$ rides on a disk of mass $6.00 \\mathrm{~m}$ and radius $R$. The disk rotates like a merry-go-round around its central axis at angular speed $\\omega_i=1.50 \\mathrm{rad} / \\mathrm{s}$. The cockroach is initially at radius $r=0.800 R$, but then it crawls out to the rim of the disk. Treat the cockroach as a particle. What then is the angular speed?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>This sample problem involves a tilted applied force, which requires that we work with components to find a frictional force. The main challenge is to sort out all the components. Figure shows a force of magnitude $F=$ $12.0 \\mathrm{~N}$ applied to an $8.00 \\mathrm{~kg}$ block at a downward angle of $\\theta=30.0^{\\circ}$. The coefficient of static friction between block and floor is $\\mu_s=0.700$; the coefficient of kinetic friction is $\\mu_k=0.400$. What is the magnitude of the frictional force on the block?",
"role": "user"
}
] |
{
"ground_truth": "10.39 N",
"style": "rule"
}
|
{
"gt_answer": "10.39 N",
"id": "scibench_multimodal--34",
"mc_options": null,
"original_question": "<image>This sample problem involves a tilted applied force, which requires that we work with components to find a frictional force. The main challenge is to sort out all the components. Figure shows a force of magnitude $F=$ $12.0 \\mathrm{~N}$ applied to an $8.00 \\mathrm{~kg}$ block at a downward angle of $\\theta=30.0^{\\circ}$. The coefficient of static friction between block and floor is $\\mu_s=0.700$; the coefficient of kinetic friction is $\\mu_k=0.400$. What is the magnitude of the frictional force on the block?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>For the function $g$ whose graph is given, state the value of $g(2)$.",
"role": "user"
}
] |
{
"ground_truth": "1",
"style": "rule"
}
|
{
"gt_answer": "1",
"id": "scibench_multimodal--35",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $g(2)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Comet Halley orbits the Sun with a period of 76 years and, in 1986, had a distance of closest approach to the Sun, its perihelion distance $R_p$, of $8.9 \\times 10^{10} \\mathrm{~m}$. Table shows that this is between the orbits of Mercury and Venus. What is the eccentricity $e$ of the orbit of comet Halley?",
"role": "user"
}
] |
{
"ground_truth": "0.97",
"style": "rule"
}
|
{
"gt_answer": "0.97",
"id": "scibench_multimodal--36",
"mc_options": null,
"original_question": "<image>Comet Halley orbits the Sun with a period of 76 years and, in 1986, had a distance of closest approach to the Sun, its perihelion distance $R_p$, of $8.9 \\times 10^{10} \\mathrm{~m}$. Table shows that this is between the orbits of Mercury and Venus. What is the eccentricity $e$ of the orbit of comet Halley?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Let\r\n$$\r\n\\mathbf{F}(x, y, z)=\\left(3 x^2 y z-3 y\\right) \\mathbf{i}+\\left(x^3 z-3 x\\right) \\mathbf{j}+\\left(x^3 y+2 z\\right) \\mathbf{k}\r\n$$\r\nEvaluate $\\int_C \\mathbf{F} \\cdot d r$, where $C$ is the curve with initial point $(0,0,2)$ and terminal point $(0,3,0)$ shown in the figure.\r\n",
"role": "user"
}
] |
{
"ground_truth": "-4",
"style": "rule"
}
|
{
"gt_answer": "-4",
"id": "scibench_multimodal--37",
"mc_options": null,
"original_question": "<image>Let\r\n$$\r\n\\mathbf{F}(x, y, z)=\\left(3 x^2 y z-3 y\\right) \\mathbf{i}+\\left(x^3 z-3 x\\right) \\mathbf{j}+\\left(x^3 y+2 z\\right) \\mathbf{k}\r\n$$\r\nEvaluate $\\int_C \\mathbf{F} \\cdot d r$, where $C$ is the curve with initial point $(0,0,2)$ and terminal point $(0,3,0)$ shown in the figure.\r\n"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Here is an example of a common technique in physics. We have a demonstration that cannot be worked out as a whole (we don't have a workable equation for it). So, we break it up into steps that can be worked separately (we have equations for them).\r\n\r\nThe ballistic pendulum was used to measure the speeds of bullets before electronic timing devices were developed. The version shown in Figure consists of a large block of wood of mass $M=5.4 \\mathrm{~kg}$, hanging from two long cords. A bullet of mass $m=9.5 \\mathrm{~g}$ is fired into the block, coming quickly to rest. The block + bullet then swing upward, their center of mass rising a vertical distance $h=6.3 \\mathrm{~cm}$ before the pendulum comes momentarily to rest at the end of its arc. What is the speed of the bullet just prior to the collision?",
"role": "user"
}
] |
{
"ground_truth": "630 m/s",
"style": "rule"
}
|
{
"gt_answer": "630 m/s",
"id": "scibench_multimodal--38",
"mc_options": null,
"original_question": "<image>Here is an example of a common technique in physics. We have a demonstration that cannot be worked out as a whole (we don't have a workable equation for it). So, we break it up into steps that can be worked separately (we have equations for them).\r\n\r\nThe ballistic pendulum was used to measure the speeds of bullets before electronic timing devices were developed. The version shown in Figure consists of a large block of wood of mass $M=5.4 \\mathrm{~kg}$, hanging from two long cords. A bullet of mass $m=9.5 \\mathrm{~g}$ is fired into the block, coming quickly to rest. The block + bullet then swing upward, their center of mass rising a vertical distance $h=6.3 \\mathrm{~cm}$ before the pendulum comes momentarily to rest at the end of its arc. What is the speed of the bullet just prior to the collision?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Fig. 4-20a, a plane moves due east while the pilot points the plane somewhat south of east, toward a steady wind that blows to the northeast. The plane has velocity $\\vec{v}_{P W}$ relative to the wind, with an airspeed (speed relative to the wind) of $215 \\mathrm{~km} / \\mathrm{h}$, directed at angle $\\theta$ south of east. The wind has velocity $\\vec{v}_{W G}$ relative to the ground with speed $65.0 \\mathrm{~km} / \\mathrm{h}$, directed $20.0^{\\circ}$ east of north. What is the magnitude of the velocity $\\vec{v}_{P G}$ of the plane relative to the ground?",
"role": "user"
}
] |
{
"ground_truth": "228 km/h",
"style": "rule"
}
|
{
"gt_answer": "228 km/h",
"id": "scibench_multimodal--39",
"mc_options": null,
"original_question": "<image>In Fig. 4-20a, a plane moves due east while the pilot points the plane somewhat south of east, toward a steady wind that blows to the northeast. The plane has velocity $\\vec{v}_{P W}$ relative to the wind, with an airspeed (speed relative to the wind) of $215 \\mathrm{~km} / \\mathrm{h}$, directed at angle $\\theta$ south of east. The wind has velocity $\\vec{v}_{W G}$ relative to the ground with speed $65.0 \\mathrm{~km} / \\mathrm{h}$, directed $20.0^{\\circ}$ east of north. What is the magnitude of the velocity $\\vec{v}_{P G}$ of the plane relative to the ground?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Some of the funniest videos on the web involve motorists sliding uncontrollably on icy roads. Here let's compare the typical stopping distances for a car sliding to a stop from an initial speed of $10.0 \\mathrm{~m} / \\mathrm{s}$ on a dry horizontal road, an icy horizontal road, and (everyone's favorite) an icy hill.\r\nHow far does the car take to slide to a stop on a horizontal road (Figure) if the coefficient of kinetic friction is $\\mu_k=0.60$, which is typical of regular tires on dry pavement? Let's neglect any effect of the air on the car, assume that the wheels lock up and the tires slide, and extend an $x$ axis in the car's direction of motion.",
"role": "user"
}
] |
{
"ground_truth": "8.50 m",
"style": "rule"
}
|
{
"gt_answer": "8.50 m",
"id": "scibench_multimodal--40",
"mc_options": null,
"original_question": "<image>Some of the funniest videos on the web involve motorists sliding uncontrollably on icy roads. Here let's compare the typical stopping distances for a car sliding to a stop from an initial speed of $10.0 \\mathrm{~m} / \\mathrm{s}$ on a dry horizontal road, an icy horizontal road, and (everyone's favorite) an icy hill.\r\nHow far does the car take to slide to a stop on a horizontal road (Figure) if the coefficient of kinetic friction is $\\mu_k=0.60$, which is typical of regular tires on dry pavement? Let's neglect any effect of the air on the car, assume that the wheels lock up and the tires slide, and extend an $x$ axis in the car's direction of motion."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure shows an overhead view of two particles moving at constant momentum along horizontal paths. Particle 1, with momentum magnitude $p_1=5.0 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$, has position vector $\\vec{r}_1$ and will pass $2.0 \\mathrm{~m}$ from point $O$. Particle 2 , with momentum magnitude $p_2=2.0 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$, has position vector $\\vec{r}_2$ and will pass $4.0 \\mathrm{~m}$ from point $O$. What is the magnitude of the net angular momentum $\\vec{L}$ about point $O$ of the two-particle system?",
"role": "user"
}
] |
{
"ground_truth": "2.0 $\\mathrm{kg} \\cdot \\mathrm{m}^2 / \\mathrm{s}$",
"style": "rule"
}
|
{
"gt_answer": "2.0 $\\mathrm{kg} \\cdot \\mathrm{m}^2 / \\mathrm{s}$",
"id": "scibench_multimodal--41",
"mc_options": null,
"original_question": "<image>Figure shows an overhead view of two particles moving at constant momentum along horizontal paths. Particle 1, with momentum magnitude $p_1=5.0 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$, has position vector $\\vec{r}_1$ and will pass $2.0 \\mathrm{~m}$ from point $O$. Particle 2 , with momentum magnitude $p_2=2.0 \\mathrm{~kg} \\cdot \\mathrm{m} / \\mathrm{s}$, has position vector $\\vec{r}_2$ and will pass $4.0 \\mathrm{~m}$ from point $O$. What is the magnitude of the net angular momentum $\\vec{L}$ about point $O$ of the two-particle system?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A spaceship of mass $m=4.50 \\times 10^3 \\mathrm{~kg}$ is in a circular Earth orbit of radius $r=8.00 \\times 10^6 \\mathrm{~m}$ and period $T_0=118.6 \\mathrm{~min}=$ $7.119 \\times 10^3 \\mathrm{~s}$ when a thruster is fired in the forward direction to decrease the speed to $96.0 \\%$ of the original speed. What is the period $T$ of the resulting elliptical orbit (Figure)?",
"role": "user"
}
] |
{
"ground_truth": "6.356 $10^3 s$",
"style": "rule"
}
|
{
"gt_answer": "6.356 $10^3 s$",
"id": "scibench_multimodal--42",
"mc_options": null,
"original_question": "<image>A spaceship of mass $m=4.50 \\times 10^3 \\mathrm{~kg}$ is in a circular Earth orbit of radius $r=8.00 \\times 10^6 \\mathrm{~m}$ and period $T_0=118.6 \\mathrm{~min}=$ $7.119 \\times 10^3 \\mathrm{~s}$ when a thruster is fired in the forward direction to decrease the speed to $96.0 \\%$ of the original speed. What is the period $T$ of the resulting elliptical orbit (Figure)?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>\"Whiplash injury\" commonly occurs in a rear-end collision where a front car is hit from behind by a second car. In the 1970s, researchers concluded that the injury was due to the occupant's head being whipped back over the top of the seat as the car was slammed forward. As a result of this finding, head restraints were built into cars, yet neck injuries in rearend collisions continued to occur.\r\n\r\nIn a recent test to study neck injury in rear-end collisions, a volunteer was strapped to a seat that was then moved abruptly to simulate a collision by a rear car moving at $10.5 \\mathrm{~km} / \\mathrm{h}$. Figure gives the accelerations of the volunteer's torso and head during the collision, which began at time $t=0$. The torso acceleration was delayed by $40 \\mathrm{~ms}$ because during that time interval the seat back had to compress against the volunteer. The head acceleration was delayed by an additional $70 \\mathrm{~ms}$. What was the torso speed when the head began to accelerate?",
"role": "user"
}
] |
{
"ground_truth": "2.0 m/s",
"style": "rule"
}
|
{
"gt_answer": "2.0 m/s",
"id": "scibench_multimodal--43",
"mc_options": null,
"original_question": "<image>\"Whiplash injury\" commonly occurs in a rear-end collision where a front car is hit from behind by a second car. In the 1970s, researchers concluded that the injury was due to the occupant's head being whipped back over the top of the seat as the car was slammed forward. As a result of this finding, head restraints were built into cars, yet neck injuries in rearend collisions continued to occur.\r\n\r\nIn a recent test to study neck injury in rear-end collisions, a volunteer was strapped to a seat that was then moved abruptly to simulate a collision by a rear car moving at $10.5 \\mathrm{~km} / \\mathrm{h}$. Figure gives the accelerations of the volunteer's torso and head during the collision, which began at time $t=0$. The torso acceleration was delayed by $40 \\mathrm{~ms}$ because during that time interval the seat back had to compress against the volunteer. The head acceleration was delayed by an additional $70 \\mathrm{~ms}$. What was the torso speed when the head began to accelerate?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Phenylalanine (Phe, 5) is a naturally occurring amino acid. What is the energy of interaction between its phenyl group and the electric dipole moment of a neighbouring peptide group? Take the distance between the groups as $4.0 \\mathrm{~nm}$ and treat the phenyl group as a benzene molecule. The magnitude of the dipole moment of the peptide group is $\\mu=1.3 \\mathrm{D}$ and the polarizability volume of benzene is $\\alpha^{\\prime}=1.04 \\times 10^{-29} \\mathrm{~m}^3$.\r\n",
"role": "user"
}
] |
{
"ground_truth": "-4.3 $10^{-28} \\mathrm{~J}$",
"style": "rule"
}
|
{
"gt_answer": "-4.3 $10^{-28} \\mathrm{~J}$",
"id": "scibench_multimodal--44",
"mc_options": null,
"original_question": "<image>Phenylalanine (Phe, 5) is a naturally occurring amino acid. What is the energy of interaction between its phenyl group and the electric dipole moment of a neighbouring peptide group? Take the distance between the groups as $4.0 \\mathrm{~nm}$ and treat the phenyl group as a benzene molecule. The magnitude of the dipole moment of the peptide group is $\\mu=1.3 \\mathrm{D}$ and the polarizability volume of benzene is $\\alpha^{\\prime}=1.04 \\times 10^{-29} \\mathrm{~m}^3$.\r\n"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure shows a safe (mass $M=430 \\mathrm{~kg}$ ) hanging by a rope (negligible mass) from a boom $(a=1.9 \\mathrm{~m}$ and $b=$ $2.5 \\mathrm{~m})$ that consists of a uniform hinged beam $(m=85 \\mathrm{~kg})$ and horizontal cable (negligible mass).\r\nWhat is the tension $T_c$ in the cable? In other words, what is the magnitude of the force $\\vec{T}_c$ on the beam from the cable?",
"role": "user"
}
] |
{
"ground_truth": "6093 N",
"style": "rule"
}
|
{
"gt_answer": "6093 N",
"id": "scibench_multimodal--45",
"mc_options": null,
"original_question": "<image>Figure shows a safe (mass $M=430 \\mathrm{~kg}$ ) hanging by a rope (negligible mass) from a boom $(a=1.9 \\mathrm{~m}$ and $b=$ $2.5 \\mathrm{~m})$ that consists of a uniform hinged beam $(m=85 \\mathrm{~kg})$ and horizontal cable (negligible mass).\r\nWhat is the tension $T_c$ in the cable? In other words, what is the magnitude of the force $\\vec{T}_c$ on the beam from the cable?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 4} g(t)$.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
{
"gt_answer": "3",
"id": "scibench_multimodal--46",
"mc_options": null,
"original_question": "<image>For the function $g$ whose graph is given, state the value of $\\lim _{t \\rightarrow 4} g(t)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>One of the most dramatic videos on the web (but entirely fictitious) supposedly shows a man sliding along a long water slide and then being launched into the air to land in a water pool. Let's attach some reasonable numbers to such a flight to calculate the velocity with which the man would have hit the water. Figure indicates the launch and landing sites and includes a superimposed coordinate system with its origin conveniently located at the launch site. From the video we take the horizontal flight distance as $D=20.0 \\mathrm{~m}$, the flight time as $t=2.50 \\mathrm{~s}$, and the launch angle as $\\theta_0=40.0^{\\circ}$. Find the magnitude of the velocity at launch and at landing.",
"role": "user"
}
] |
{
"ground_truth": "10.44 m/s",
"style": "rule"
}
|
{
"gt_answer": "10.44 m/s",
"id": "scibench_multimodal--47",
"mc_options": null,
"original_question": "<image>One of the most dramatic videos on the web (but entirely fictitious) supposedly shows a man sliding along a long water slide and then being launched into the air to land in a water pool. Let's attach some reasonable numbers to such a flight to calculate the velocity with which the man would have hit the water. Figure indicates the launch and landing sites and includes a superimposed coordinate system with its origin conveniently located at the launch site. From the video we take the horizontal flight distance as $D=20.0 \\mathrm{~m}$, the flight time as $t=2.50 \\mathrm{~s}$, and the launch angle as $\\theta_0=40.0^{\\circ}$. Find the magnitude of the velocity at launch and at landing."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure shows a uniform disk, with mass $M=2.5 \\mathrm{~kg}$ and radius $R=20 \\mathrm{~cm}$, mounted on a fixed horizontal axle. A block with mass $m=1.2 \\mathrm{~kg}$ hangs from a massless cord that is wrapped around the rim of the disk. Find the tension in the cord. The cord does not slip, and there is no friction at the axle.",
"role": "user"
}
] |
{
"ground_truth": "6.0 N",
"style": "rule"
}
|
{
"gt_answer": "6.0 N",
"id": "scibench_multimodal--48",
"mc_options": null,
"original_question": "<image>Figure shows a uniform disk, with mass $M=2.5 \\mathrm{~kg}$ and radius $R=20 \\mathrm{~cm}$, mounted on a fixed horizontal axle. A block with mass $m=1.2 \\mathrm{~kg}$ hangs from a massless cord that is wrapped around the rim of the disk. Find the tension in the cord. The cord does not slip, and there is no friction at the axle."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Figure, suppose that Barbara's velocity relative to Alex is a constant $v_{B A}=52 \\mathrm{~km} / \\mathrm{h}$ and car $P$ is moving in the negative direction of the $x$ axis.\r\n(a) If Alex measures a constant $v_{P A}=-78 \\mathrm{~km} / \\mathrm{h}$ for car $P$, what velocity $v_{P B}$ will Barbara measure?",
"role": "user"
}
] |
{
"ground_truth": "-130 km/h",
"style": "rule"
}
|
{
"gt_answer": "-130 km/h",
"id": "scibench_multimodal--49",
"mc_options": null,
"original_question": "<image>In Figure, suppose that Barbara's velocity relative to Alex is a constant $v_{B A}=52 \\mathrm{~km} / \\mathrm{h}$ and car $P$ is moving in the negative direction of the $x$ axis.\r\n(a) If Alex measures a constant $v_{P A}=-78 \\mathrm{~km} / \\mathrm{h}$ for car $P$, what velocity $v_{P B}$ will Barbara measure?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure is an overhead view of the path taken by a race car driver as his car collides with the racetrack wall. Just before the collision, he is traveling at speed $v_i=70 \\mathrm{~m} / \\mathrm{s}$ along a straight line at $30^{\\circ}$ from the wall. Just after the collision, he is traveling at speed $v_f=50 \\mathrm{~m} / \\mathrm{s}$ along a straight line at $10^{\\circ}$ from the wall. His mass $m$ is $80 \\mathrm{~kg}$. The collision lasts for $14 \\mathrm{~ms}$. What is the magnitude of the average force on the driver during the collision?",
"role": "user"
}
] |
{
"ground_truth": "2.583 $10^5$ N",
"style": "rule"
}
|
{
"gt_answer": "2.583 $10^5$ N",
"id": "scibench_multimodal--50",
"mc_options": null,
"original_question": "<image>Figure is an overhead view of the path taken by a race car driver as his car collides with the racetrack wall. Just before the collision, he is traveling at speed $v_i=70 \\mathrm{~m} / \\mathrm{s}$ along a straight line at $30^{\\circ}$ from the wall. Just after the collision, he is traveling at speed $v_f=50 \\mathrm{~m} / \\mathrm{s}$ along a straight line at $10^{\\circ}$ from the wall. His mass $m$ is $80 \\mathrm{~kg}$. The collision lasts for $14 \\mathrm{~ms}$. What is the magnitude of the average force on the driver during the collision?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A raindrop with radius $R=1.5 \\mathrm{~mm}$ falls from a cloud that is at height $h=1200 \\mathrm{~m}$ above the ground. The drag coefficient $C$ for the drop is 0.60 . Assume that the drop is spherical throughout its fall. The density of water $\\rho_w$ is $1000 \\mathrm{~kg} / \\mathrm{m}^3$, and the density of air $\\rho_a$ is $1.2 \\mathrm{~kg} / \\mathrm{m}^3$.\r\nAs the Table indicates, the raindrop reaches terminal speed after falling just a few meters. What is the terminal speed?",
"role": "user"
}
] |
{
"ground_truth": "7.4 m/s",
"style": "rule"
}
|
{
"gt_answer": "7.4 m/s",
"id": "scibench_multimodal--51",
"mc_options": null,
"original_question": "<image>A raindrop with radius $R=1.5 \\mathrm{~mm}$ falls from a cloud that is at height $h=1200 \\mathrm{~m}$ above the ground. The drag coefficient $C$ for the drop is 0.60 . Assume that the drop is spherical throughout its fall. The density of water $\\rho_w$ is $1000 \\mathrm{~kg} / \\mathrm{m}^3$, and the density of air $\\rho_a$ is $1.2 \\mathrm{~kg} / \\mathrm{m}^3$.\r\nAs the Table indicates, the raindrop reaches terminal speed after falling just a few meters. What is the terminal speed?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A modern race car is designed so that the passing air pushes down on it, allowing the car to travel much faster through a flat turn in a Grand Prix without friction failing. This downward push is called negative lift. Can a race car have so much negative lift that it could be driven upside down on a long ceiling, as done fictionally by a sedan in the first Men in Black movie?\r\n\r\nFigure represents a Grand Prix race car of mass $m=600 \\mathrm{~kg}$ as it travels on a flat track in a circular arc of radius $R=100 \\mathrm{~m}$. Because of the shape of the car and the wings on it, the passing air exerts a negative lift $\\vec{F}_L$ downward on the car. The coefficient of static friction between the tires and the track is 0.75 . (Assume that the forces on the four tires are identical.)\r\nIf the car is on the verge of sliding out of the turn when its speed is $28.6 \\mathrm{~m} / \\mathrm{s}$, what is the magnitude of the negative lift $\\vec{F}_L$ acting downward on the car?",
"role": "user"
}
] |
{
"ground_truth": "663.7 N",
"style": "rule"
}
|
{
"gt_answer": "663.7 N",
"id": "scibench_multimodal--52",
"mc_options": null,
"original_question": "<image>A modern race car is designed so that the passing air pushes down on it, allowing the car to travel much faster through a flat turn in a Grand Prix without friction failing. This downward push is called negative lift. Can a race car have so much negative lift that it could be driven upside down on a long ceiling, as done fictionally by a sedan in the first Men in Black movie?\r\n\r\nFigure represents a Grand Prix race car of mass $m=600 \\mathrm{~kg}$ as it travels on a flat track in a circular arc of radius $R=100 \\mathrm{~m}$. Because of the shape of the car and the wings on it, the passing air exerts a negative lift $\\vec{F}_L$ downward on the car. The coefficient of static friction between the tires and the track is 0.75 . (Assume that the forces on the four tires are identical.)\r\nIf the car is on the verge of sliding out of the turn when its speed is $28.6 \\mathrm{~m} / \\mathrm{s}$, what is the magnitude of the negative lift $\\vec{F}_L$ acting downward on the car?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>When a spring does work on an object, we cannot find the work by simply multiplying the spring force by the object's displacement. The reason is that there is no one value for the force-it changes. However, we can split the displacement up into an infinite number of tiny parts and then approximate the force in each as being constant. Integration sums the work done in all those parts. Here we use the generic result of the integration.\r\n\r\nIn Figure, a cumin canister of mass $m=0.40 \\mathrm{~kg}$ slides across a horizontal frictionless counter with speed $v=0.50 \\mathrm{~m} / \\mathrm{s}$. It then runs into and compresses a spring of spring constant $k=750 \\mathrm{~N} / \\mathrm{m}$. When the canister is momentarily stopped by the spring, by what distance $d$ is the spring compressed?",
"role": "user"
}
] |
{
"ground_truth": "1.2 $10^{-2}$ m",
"style": "rule"
}
|
{
"gt_answer": "1.2 $10^{-2}$ m",
"id": "scibench_multimodal--53",
"mc_options": null,
"original_question": "<image>When a spring does work on an object, we cannot find the work by simply multiplying the spring force by the object's displacement. The reason is that there is no one value for the force-it changes. However, we can split the displacement up into an infinite number of tiny parts and then approximate the force in each as being constant. Integration sums the work done in all those parts. Here we use the generic result of the integration.\r\n\r\nIn Figure, a cumin canister of mass $m=0.40 \\mathrm{~kg}$ slides across a horizontal frictionless counter with speed $v=0.50 \\mathrm{~m} / \\mathrm{s}$. It then runs into and compresses a spring of spring constant $k=750 \\mathrm{~N} / \\mathrm{m}$. When the canister is momentarily stopped by the spring, by what distance $d$ is the spring compressed?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The magnitude of the acceleration vector a is $10 \\mathrm{~cm} / \\mathrm{s}^2$. Use the figure to estimate the tangential components of $\\mathbf{a}$.\r\n",
"role": "user"
}
] |
{
"ground_truth": "4.5 $\\mathrm{cm}/\\mathrm{s^2}$",
"style": "rule"
}
|
{
"gt_answer": "4.5 $\\mathrm{cm}/\\mathrm{s^2}$",
"id": "scibench_multimodal--54",
"mc_options": null,
"original_question": "<image>The magnitude of the acceleration vector a is $10 \\mathrm{~cm} / \\mathrm{s}^2$. Use the figure to estimate the tangential components of $\\mathbf{a}$.\r\n"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure shows an arrangement of three particles, particle 1 of mass $m_1=6.0 \\mathrm{~kg}$ and particles 2 and 3 of mass $m_2=$ $m_3=4.0 \\mathrm{~kg}$, and distance $a=2.0 \\mathrm{~cm}$. What is the net gravitational force $\\vec{F}_{1, \\text { net }}$ on particle 1 due to the other particles?",
"role": "user"
}
] |
{
"ground_truth": "4.1 $10^{-6} \\mathrm{~N}$",
"style": "rule"
}
|
{
"gt_answer": "4.1 $10^{-6} \\mathrm{~N}$",
"id": "scibench_multimodal--55",
"mc_options": null,
"original_question": "<image>Figure shows an arrangement of three particles, particle 1 of mass $m_1=6.0 \\mathrm{~kg}$ and particles 2 and 3 of mass $m_2=$ $m_3=4.0 \\mathrm{~kg}$, and distance $a=2.0 \\mathrm{~cm}$. What is the net gravitational force $\\vec{F}_{1, \\text { net }}$ on particle 1 due to the other particles?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>In Figure, a rescue plane flies at $198 \\mathrm{~km} / \\mathrm{h}(=55.0 \\mathrm{~m} / \\mathrm{s})$ and constant height $h=500 \\mathrm{~m}$ toward a point directly over a victim, where a rescue capsule is to land.\r\nWhat should be the angle $\\phi$ of the pilot's line of sight to the victim when the capsule release is made?",
"role": "user"
}
] |
{
"ground_truth": "48.0 $^{\\circ}$",
"style": "rule"
}
|
{
"gt_answer": "48.0 $^{\\circ}$",
"id": "scibench_multimodal--56",
"mc_options": null,
"original_question": "<image>In Figure, a rescue plane flies at $198 \\mathrm{~km} / \\mathrm{h}(=55.0 \\mathrm{~m} / \\mathrm{s})$ and constant height $h=500 \\mathrm{~m}$ toward a point directly over a victim, where a rescue capsule is to land.\r\nWhat should be the angle $\\phi$ of the pilot's line of sight to the victim when the capsule release is made?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Use the given graph of $f$ to find the largest number $\\delta$ such that if $\\quad|x-1|<\\delta \\quad$ then $\\quad|f(x)-1|<0.2$.",
"role": "user"
}
] |
{
"ground_truth": "0.1",
"style": "rule"
}
|
{
"gt_answer": "0.1",
"id": "scibench_multimodal--57",
"mc_options": null,
"original_question": "<image>Use the given graph of $f$ to find the largest number $\\delta$ such that if $\\quad|x-1|<\\delta \\quad$ then $\\quad|f(x)-1|<0.2$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Figure shows a block $S$ (the sliding block) with mass $M=3.3 \\mathrm{~kg}$. The block is free to move along a horizontal frictionless surface and connected, by a cord that wraps over a frictionless pulley, to a second block $H$ (the hanging block), with mass $m=2.1 \\mathrm{~kg}$. The cord and pulley have negligible masses compared to the blocks (they are \"massless\"). The hanging block $H$ falls as the sliding block $S$ accelerates to the right. Find the tension in the cord.",
"role": "user"
}
] |
{
"ground_truth": "13 N",
"style": "rule"
}
|
{
"gt_answer": "13 N",
"id": "scibench_multimodal--58",
"mc_options": null,
"original_question": "<image>Figure shows a block $S$ (the sliding block) with mass $M=3.3 \\mathrm{~kg}$. The block is free to move along a horizontal frictionless surface and connected, by a cord that wraps over a frictionless pulley, to a second block $H$ (the hanging block), with mass $m=2.1 \\mathrm{~kg}$. The cord and pulley have negligible masses compared to the blocks (they are \"massless\"). The hanging block $H$ falls as the sliding block $S$ accelerates to the right. Find the tension in the cord."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>For the function $f$ whose graph is given, state $\\lim _{x \\rightarrow \\infty} f(x)$.",
"role": "user"
}
] |
{
"ground_truth": "-2",
"style": "rule"
}
|
{
"gt_answer": "-2",
"id": "scibench_multimodal--59",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state $\\lim _{x \\rightarrow \\infty} f(x)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>For the function $f$ whose graph is given, state $\\lim _{x \\rightarrow-\\infty} f(x)$.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
{
"gt_answer": "2",
"id": "scibench_multimodal--60",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state $\\lim _{x \\rightarrow-\\infty} f(x)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2002 to 2006.",
"role": "user"
}
] |
{
"ground_truth": "23 million/year",
"style": "rule"
}
|
{
"gt_answer": "23 million/year",
"id": "scibench_multimodal--61",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2002 to 2006."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2002 to 2004.",
"role": "user"
}
] |
{
"ground_truth": "20.5 million/year",
"style": "rule"
}
|
{
"gt_answer": "20.5 million/year",
"id": "scibench_multimodal--62",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2002 to 2004."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Use the given graphs of $f$ and $g$ to evaluate $f(g(2))$.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
{
"gt_answer": "4",
"id": "scibench_multimodal--63",
"mc_options": null,
"original_question": "<image>Use the given graphs of $f$ and $g$ to evaluate $f(g(2))$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2000 to 2002.",
"role": "user"
}
] |
{
"ground_truth": "16 million/year",
"style": "rule"
}
|
{
"gt_answer": "16 million/year",
"id": "scibench_multimodal--64",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Find the average rate of cell phone growth from 2000 to 2002."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Estimate the instantaneous rate of growth in 2002 by taking the average of two average rates of change with units.",
"role": "user"
}
] |
{
"ground_truth": "18.25 million/year",
"style": "rule"
}
|
{
"gt_answer": "18.25 million/year",
"id": "scibench_multimodal--65",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Estimate the instantaneous rate of growth in 2002 by taking the average of two average rates of change with units."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Estimate the instantaneous rate of growth in 2002 by measuring the slope of a tangent.",
"role": "user"
}
] |
{
"ground_truth": "17 million/year",
"style": "rule"
}
|
{
"gt_answer": "17 million/year",
"id": "scibench_multimodal--66",
"mc_options": null,
"original_question": "<image>The number $N$ of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.). Estimate the instantaneous rate of growth in 2002 by measuring the slope of a tangent."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Let $T(t)$ be the temperature (in ${ }^{\\circ} \\mathrm{F}$ ) in Phoenix $t$ hours after midnight on September 10, 2008. The table shows values of this function recorded every two hours. Estimate the value of $T^{\\prime}(8)$.",
"role": "user"
}
] |
{
"ground_truth": "3.75 $^{\\circ} \\mathrm{F} / \\mathrm{h}$",
"style": "rule"
}
|
{
"gt_answer": "3.75 $^{\\circ} \\mathrm{F} / \\mathrm{h}$",
"id": "scibench_multimodal--67",
"mc_options": null,
"original_question": "<image>Let $T(t)$ be the temperature (in ${ }^{\\circ} \\mathrm{F}$ ) in Phoenix $t$ hours after midnight on September 10, 2008. The table shows values of this function recorded every two hours. Estimate the value of $T^{\\prime}(8)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow 2^{+}} f(x)$.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
{
"gt_answer": "3",
"id": "scibench_multimodal--68",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow 2^{+}} f(x)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow-3^{+}} f(x)$.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
{
"gt_answer": "0",
"id": "scibench_multimodal--69",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow-3^{+}} f(x)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow 4} f(x)$.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
{
"gt_answer": "2",
"id": "scibench_multimodal--70",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow 4} f(x)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow \\infty} f(x)$.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
{
"gt_answer": "4",
"id": "scibench_multimodal--71",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow \\infty} f(x)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow-\\infty} f(x)$.",
"role": "user"
}
] |
{
"ground_truth": "-1",
"style": "rule"
}
|
{
"gt_answer": "-1",
"id": "scibench_multimodal--72",
"mc_options": null,
"original_question": "<image>The graph of $f$ is given. Find the limit, $\\lim _{x \\rightarrow-\\infty} f(x)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(x) g(x)$ and $v(x)=f(x) / g(x)$. Find $u^{\\prime}(1)$.",
"role": "user"
}
] |
{
"ground_truth": "0",
"style": "rule"
}
|
{
"gt_answer": "0",
"id": "scibench_multimodal--73",
"mc_options": null,
"original_question": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(x) g(x)$ and $v(x)=f(x) / g(x)$. Find $u^{\\prime}(1)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Find the value of $C$ in the exponential function $f(x)=C a^x$ whose graph is given.",
"role": "user"
}
] |
{
"ground_truth": "3",
"style": "rule"
}
|
{
"gt_answer": "3",
"id": "scibench_multimodal--74",
"mc_options": null,
"original_question": "<image>Find the value of $C$ in the exponential function $f(x)=C a^x$ whose graph is given."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(x) g(x)$ and $v(x)=f(x) / g(x)$. Find $v^{\\prime}(5)$.",
"role": "user"
}
] |
{
"ground_truth": "$ -\\frac{2}{3}$",
"style": "rule"
}
|
{
"gt_answer": "$ -\\frac{2}{3}$",
"id": "scibench_multimodal--75",
"mc_options": null,
"original_question": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(x) g(x)$ and $v(x)=f(x) / g(x)$. Find $v^{\\prime}(5)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(g(x)), v(x)=g(f(x))$, and $w(x)=g(g(x))$. Find the derivative, $u^{\\prime}(1)$.",
"role": "user"
}
] |
{
"ground_truth": "$\\frac{3}{4}$",
"style": "rule"
}
|
{
"gt_answer": "$\\frac{3}{4}$",
"id": "scibench_multimodal--76",
"mc_options": null,
"original_question": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(g(x)), v(x)=g(f(x))$, and $w(x)=g(g(x))$. Find the derivative, $u^{\\prime}(1)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(g(x)), v(x)=g(f(x))$, and $w(x)=g(g(x))$. Find the derivative, $w^{\\prime}(1)$.",
"role": "user"
}
] |
{
"ground_truth": "-2",
"style": "rule"
}
|
{
"gt_answer": "-2",
"id": "scibench_multimodal--77",
"mc_options": null,
"original_question": "<image>If $f$ and $g$ are the functions whose graphs are shown, let $u(x)=f(g(x)), v(x)=g(f(x))$, and $w(x)=g(g(x))$. Find the derivative, $w^{\\prime}(1)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>If $g(x)=\\sqrt{f(x)}$, where the graph of $f$ is shown, evaluate $g^{\\prime}(3)$.",
"role": "user"
}
] |
{
"ground_truth": "$-\\frac{1}{6} \\sqrt{2}$",
"style": "rule"
}
|
{
"gt_answer": "$-\\frac{1}{6} \\sqrt{2}$",
"id": "scibench_multimodal--78",
"mc_options": null,
"original_question": "<image>If $g(x)=\\sqrt{f(x)}$, where the graph of $f$ is shown, evaluate $g^{\\prime}(3)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The table gives the population of the world in the 20th century. Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines.",
"role": "user"
}
] |
{
"ground_truth": "16 million/year",
"style": "rule"
}
|
{
"gt_answer": "16 million/year",
"id": "scibench_multimodal--79",
"mc_options": null,
"original_question": "<image>The table gives the population of the world in the 20th century. Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The table gives the population of the world in the 20th century. Estimate the rate of growth in 1985.",
"role": "user"
}
] |
{
"ground_truth": "81.62 million/year",
"style": "rule"
}
|
{
"gt_answer": "81.62 million/year",
"id": "scibench_multimodal--80",
"mc_options": null,
"original_question": "<image>The table gives the population of the world in the 20th century. Estimate the rate of growth in 1985."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900.",
"role": "user"
}
] |
{
"ground_truth": "1508 million",
"style": "rule"
}
|
{
"gt_answer": "1508 million",
"id": "scibench_multimodal--81",
"mc_options": null,
"original_question": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1750 and 1800 to predict the world population in 1900."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950. ",
"role": "user"
}
] |
{
"ground_truth": "2161 million",
"style": "rule"
}
|
{
"gt_answer": "2161 million",
"id": "scibench_multimodal--82",
"mc_options": null,
"original_question": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1850 and 1900 to predict the world population in 1950. "
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000. ",
"role": "user"
}
] |
{
"ground_truth": "3972 million",
"style": "rule"
}
|
{
"gt_answer": "3972 million",
"id": "scibench_multimodal--83",
"mc_options": null,
"original_question": "<image>The table gives estimates of the world population, in millions, from 1750 to 2000. Use the exponential model and the population figures for 1900 and 1950 to predict the world population in 2000. "
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Suppose that the only information we have about a function $f$ is that $f(1)=5$ and the graph of its derivative is as shown. Use a linear approximation to estimate $f(0.9)$.",
"role": "user"
}
] |
{
"ground_truth": "4.8",
"style": "rule"
}
|
{
"gt_answer": "4.8",
"id": "scibench_multimodal--84",
"mc_options": null,
"original_question": "<image>Suppose that the only information we have about a function $f$ is that $f(1)=5$ and the graph of its derivative is as shown. Use a linear approximation to estimate $f(0.9)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Let $f$ be the function whose graph is given. Estimate the value of $f(2)$.",
"role": "user"
}
] |
{
"ground_truth": "2.7",
"style": "rule"
}
|
{
"gt_answer": "2.7",
"id": "scibench_multimodal--85",
"mc_options": null,
"original_question": "<image>Let $f$ be the function whose graph is given. Estimate the value of $f(2)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Use the graph to state the absolute and local maximum",
"role": "user"
}
] |
{
"ground_truth": "5",
"style": "rule"
}
|
{
"gt_answer": "5",
"id": "scibench_multimodal--86",
"mc_options": null,
"original_question": "<image>Use the graph to state the absolute and local maximum"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Use the graph of $f$ to estimate smallest value of $c$ that satisfy the conclusion of the Mean Value Theorem for the interval $[0,8]$.",
"role": "user"
}
] |
{
"ground_truth": "0.3",
"style": "rule"
}
|
{
"gt_answer": "0.3",
"id": "scibench_multimodal--87",
"mc_options": null,
"original_question": "<image>Use the graph of $f$ to estimate smallest value of $c$ that satisfy the conclusion of the Mean Value Theorem for the interval $[0,8]$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>Use the graphs of $f$ and $g$ and their tangent lines at $(2,0)$ to find $\\lim _{x \\rightarrow 2} \\frac{f(x)}{g(x)}$.",
"role": "user"
}
] |
{
"ground_truth": "$\\frac{9}{4}$",
"style": "rule"
}
|
{
"gt_answer": "$\\frac{9}{4}$",
"id": "scibench_multimodal--88",
"mc_options": null,
"original_question": "<image>Use the graphs of $f$ and $g$ and their tangent lines at $(2,0)$ to find $\\lim _{x \\rightarrow 2} \\frac{f(x)}{g(x)}$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A point $P$ needs to be located somewhere on the line $A D$ so that the total length $L$ of cables linking $P$ to the points $A, B$, and $C$ is minimized (see the figure). By expressing $L$ as a function of $x=|A P|$ and using the graphs of $L$ and $d L / d x$, estimate the minimum value of $L$.",
"role": "user"
}
] |
{
"ground_truth": "9.35",
"style": "rule"
}
|
{
"gt_answer": "9.35",
"id": "scibench_multimodal--89",
"mc_options": null,
"original_question": "<image>A point $P$ needs to be located somewhere on the line $A D$ so that the total length $L$ of cables linking $P$ to the points $A, B$, and $C$ is minimized (see the figure). By expressing $L$ as a function of $x=|A P|$ and using the graphs of $L$ and $d L / d x$, estimate the minimum value of $L$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The upper right-hand corner of a piece of paper, $12 \\mathrm{in}$. by 8 in., as in the figure, is folded over to the bottom edge. What value of $x$ will to minimize $y$ ?",
"role": "user"
}
] |
{
"ground_truth": "6 in",
"style": "rule"
}
|
{
"gt_answer": "6 in",
"id": "scibench_multimodal--90",
"mc_options": null,
"original_question": "<image>The upper right-hand corner of a piece of paper, $12 \\mathrm{in}$. by 8 in., as in the figure, is folded over to the bottom edge. What value of $x$ will to minimize $y$ ?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image> Where should the point $P$ be chosen on the line segment $A B$ so as to maximize the angle $\\theta$ ?",
"role": "user"
}
] |
{
"ground_truth": "$5-2 \\sqrt{5}$",
"style": "rule"
}
|
{
"gt_answer": "$5-2 \\sqrt{5}$",
"id": "scibench_multimodal--91",
"mc_options": null,
"original_question": "<image> Where should the point $P$ be chosen on the line segment $A B$ so as to maximize the angle $\\theta$ ?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A light is to be placed atop a pole of height $h$ feet to illuminate a busy traffic circle, which has a radius of $40 \\mathrm{ft}$. The intensity of illumination $I$ at any point $P$ on the circle is directly proportional to the cosine of the angle $\\theta$ (see the figure) and inversely proportional to the square of the distance $d$ from the source. How tall should the light pole be to maximize $I$?",
"role": "user"
}
] |
{
"ground_truth": "28 ft",
"style": "rule"
}
|
{
"gt_answer": "28 ft",
"id": "scibench_multimodal--92",
"mc_options": null,
"original_question": "<image>A light is to be placed atop a pole of height $h$ feet to illuminate a busy traffic circle, which has a radius of $40 \\mathrm{ft}$. The intensity of illumination $I$ at any point $P$ on the circle is directly proportional to the cosine of the angle $\\theta$ (see the figure) and inversely proportional to the square of the distance $d$ from the source. How tall should the light pole be to maximize $I$?"
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower estimate for the distance that she traveled during these three seconds.",
"role": "user"
}
] |
{
"ground_truth": "34.7",
"style": "rule"
}
|
{
"gt_answer": "34.7",
"id": "scibench_multimodal--93",
"mc_options": null,
"original_question": "<image>The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower estimate for the distance that she traveled during these three seconds."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied.",
"role": "user"
}
] |
{
"ground_truth": "155 ft",
"style": "rule"
}
|
{
"gt_answer": "155 ft",
"id": "scibench_multimodal--94",
"mc_options": null,
"original_question": "<image>The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the car while the brakes are applied."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with right endpoints.",
"role": "user"
}
] |
{
"ground_truth": "6",
"style": "rule"
}
|
{
"gt_answer": "6",
"id": "scibench_multimodal--95",
"mc_options": null,
"original_question": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with right endpoints."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>For the function $f$ whose graph is given, state the value of $\\lim _{x \\rightarrow 1} f(x)$.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
{
"gt_answer": "2",
"id": "scibench_multimodal--96",
"mc_options": null,
"original_question": "<image>For the function $f$ whose graph is given, state the value of $\\lim _{x \\rightarrow 1} f(x)$."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with left endpoints.",
"role": "user"
}
] |
{
"ground_truth": "4",
"style": "rule"
}
|
{
"gt_answer": "4",
"id": "scibench_multimodal--97",
"mc_options": null,
"original_question": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with left endpoints."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with midpoints.",
"role": "user"
}
] |
{
"ground_truth": "2",
"style": "rule"
}
|
{
"gt_answer": "2",
"id": "scibench_multimodal--98",
"mc_options": null,
"original_question": "<image>The graph of a function $f$ is given. Estimate $\\int_0^{10} f(x) d x$ using five subintervals with midpoints."
}
|
|
scibench_multimodal
|
[
{
"content": "<image>A table of values of an increasing function $f$ is shown. Use the table to find lower estimates for $\\int_{10}^{30} f(x) d x$.",
"role": "user"
}
] |
{
"ground_truth": "-64",
"style": "rule"
}
|
{
"gt_answer": "-64",
"id": "scibench_multimodal--99",
"mc_options": null,
"original_question": "<image>A table of values of an increasing function $f$ is shown. Use the table to find lower estimates for $\\int_{10}^{30} f(x) d x$."
}
|
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