Question

Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls, while in air

Answer 1

Step 1: Given:

$a_1=a_2=g$(Because balls are thrown in air i.e. under gravity)

Step 2: Acceleration of the center of mass:
$a_{cm}=\frac{m_1{a}_1+m_2{a}_2}{m_1+m_2}$

Here, $m_1$ is the mass of particle one, $a_1$ is the acceleration of particle one, $m_2$ is the mass of second particle, and $a_2$ is an acceleration of the second particle.

Step 3: Calculate the acceleration of the center of mass:

$$\begin{gathered} a_{cm}=\frac{m_{1}g+m_{2}g}{m_1+m_2} \\ =\frac{\left(m_1+m_2\right)g}{m_1+m_2} \\ =g \end{gathered}$$

Hence, the acceleration of the center of mass is equal to g.