Question

Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls while in air
(a) depends on the direction of the motion of the balls
(b) depends on the masses of the two balls
(c) depends on the speeds of the two balls
(d) is equal to g.

Answer 1

(d) is equal to g

The acceleration of the centre of mass of two balls having masses m₁ and m₂ is given by
$$\begin{gathered} a_{\mathrm{cm}}=\frac{m_1{{\displaystyle \overrightarrow{a}}}_1+m_2{{\displaystyle \overrightarrow{a}}}_2}{m_1+m_2} \\ =\frac{m_{1}g+m_{2}g}{m_1+m_2} \\ =g \end{gathered}$$