text: ## Q. 7.10
  
  CERES
  
  GOAL Relate Newton’s universal law of gravity to $m g$ and show how $g$ changes with position.
  
  PROBLEM An astronaut standing on the surface of Ceres, the largest asteroid, drops a rock from a height of $10.0 \mathrm{~m}$. It takes $8.06 \mathrm{~s}$ to hit the ground. (a) Calculate the acceleration of gravity on Ceres. (b) Find the mass of Ceres, given that the radius of Ceres is $R_C=5.10 \times 10^2 \mathrm{~km}$. (c) Calculate the gravitational acceleration $50.0 \mathrm{~km}$ from the surface of Ceres.
  
  STRATEGY Part (a) is a review of one-dimensional kinematics. In part (b) the weight of an object, $w=m g$, is the same as the magnitude of the force given by the universal law of gravity. Solve for the unknown mass of Ceres, after which the answer for (c) can be found by substitution into the universal law of gravity, Equation 7.21.
  
  $F = G \frac{m_1 m_2}{r^2}$      [7.21]
  
  The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
  Our explanations are based on the best information we have, but they may not always be right or fit every situation.
  The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
  
  Question: 7.13
  
  Question: 7.12
  
  Question: 7.11
  
  Question: 7.9
  
  Question: 7.8
  
  Question: 7.7
  
  Question: 7.6
  
  Question: 7.AP.2
  
  Question: 7.5
  
  Question: 7.4
explanation: The document contains a detailed problem statement and strategy for solving a physics problem related to gravity on Ceres, an asteroid. The problem has multiple parts (a, b, c) and involves calculations for the acceleration of gravity, the mass of Ceres, and the gravitational acceleration at a specific distance from the surface. The document also lists several other questions without providing their content or answers.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ## Q. 7.10
  
  CERES
  
  GOAL Relate Newton’s universal law of gravity to $m g$ and show how $g$ changes with position.
  
  PROBLEM An astronaut standing on the surface of Ceres, the largest asteroid, drops a rock from a height of $10.0 \mathrm{~m}$. It takes $8.06 \mathrm{~s}$ to hit the ground. (a) Calculate the acceleration of gravity on Ceres. (b) Find the mass of Ceres, given that the radius of Ceres is $R_C=5.10 \times 10^2 \mathrm{~km}$. (c) Calculate the gravitational acceleration $50.0 \mathrm{~km}$ from the surface of Ceres.
  
  STRATEGY Part (a) is a review of one-dimensional kinematics. In part (b) the weight of an object, $w=m g$, is the same as the magnitude of the force given by the universal law of gravity. Solve for the unknown mass of Ceres, after which the answer for (c) can be found by substitution into the universal law of gravity, Equation 7.21.
  
  $F = G \frac{m_1 m_2}{r^2}$      [7.21]
  
  The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
  Our explanations are based on the best information we have, but they may not always be right or fit every situation.
  The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
  
  Question: 7.13
  
  Question: 7.12
  
  Question: 7.11
  
  Question: 7.9
  
  Question: 7.8
  
  Question: 7.7
  
  Question: 7.6
  
  Question: 7.AP.2
  
  Question: 7.5
  
  Question: 7.4
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a detailed problem statement and strategy for solving a physics problem related to gravity on Ceres, an asteroid. The problem has multiple parts (a, b, c) and involves calculations for the acceleration of gravity, the mass of Ceres, and the gravitational acceleration at a specific distance from the surface. The document also lists several other questions without providing their content or answers.
  
  Label: multiple-question-and-answer