Question

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

• A. depends on the masses of the two balls
• B. depends on the speeds of the two balls
• C. is equal to $g$ (Acceleration due to gravity)
• D. depends on the direction of motion of the two balls.

Answer 1

Answer: (C)

is equal to $g$ (Acceleration due to gravity)

Answer 2

We know that,
Acceleration of centre of mass
$a _{ cm }=\frac{m_{1} a _{1}+m_{2} a _{2}}{m_{1}+m_{2}}$
Here, $a_{1}=a_{2}=g$ (Because balls are thiown in air i.e. under the gravity)
$a _{ cm }=\frac{m_{1} g+m_{2} g}{m_{1}+m_{2}}$
$a_{ cm }=\frac{g\left(m_{1}+m_{2}\right)}{m_{1}+m_{2}}$
$a _{ cm }=g$