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Newton's Laws for System of Particles

A particle of...

Question

A particle of mass m is thrown horizontally from the top of a tower and another particle of mass $2 m$ is thrown vertically upward. The acceleration of centre of mass is?

A

g

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B

\frac{9 g}{3}

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C

\frac{2 g}{3}

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D

\frac{g}{2}

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Solution

The correct option is A g
Both the particles experience downward acceleration due to gravity $g$ .
Acceleration of centre of mass $a_{c m} = \frac{m_{1} a_{1} + m_{2} a_{2}}{m_{1} + m_{2}}$
Or $a_{c m} = \frac{m (g) + 2 m (g)}{m + 2 m} = g$ (downwards)

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