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Q.
Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls when in air
NTA AbhyasNTA Abhyas 2022
Solution:
We know that,
Acceleration of centre of mass
$a_{c m}=\frac{m_{1} a_{1} + m_{2} a_{2}}{m_{1} + m_{2}}$
Here, $a_{1}=a_{2}=g$ (Because balls are thrown in air i.e. under the gravity)
$a_{c m}=\frac{m_{1} g + m_{2} g}{m_{1} + m_{2}}$
$a_{c m}=\frac{g \left(m_{1} + m_{2}\right)}{m_{1} + m_{2}}$
$a_{c m}=g$