1. Gavriil decided to weigh a football, but he only had weights of 150 g, a long light ruler with the markings at the ends worn off, a pencil, and many threads at his disposal. He suspended the ball from one end of the ruler and the weight from the other, and balanced the ruler on the pencil. Then he attached a second weight to the first, and to restore balance, he had to move the pencil 6 cm. When a third weight was attached to the first two, and the pencil was moved another 4 cm, balance was restored again. Calculate the mass of the ball, as Gavriil did.
1. Let the distances from the pencil to the ball and to the weight be $l_{1}$ and $l_{2}$ respectively at the first equilibrium. Denote the magnitude of the first shift by $x$, and the total shift over two times by $y$. Then the three conditions of lever equilibrium will be:

$$
\begin{gathered}
M l_{1}=m l_{2} \\
M\left(l_{1}+x\right)=2 m\left(l_{2}-x\right) \\
M\left(l_{1}+y\right)=3 m\left(l_{2}-y\right)
\end{gathered}
$$

Subtracting the first equation from the second and third, we get:

$$
\begin{gathered}
M x=m l_{2}-2 m x \\
M y=2 m l_{2}-3 m y
\end{gathered}
$$

From this,

$$
M=\frac{3 y-4 x}{2 x-y} m=600 \text { g. }
$$

In the variant with the football, the formula is the same, the answer is 450 g.