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Newton's Laws for System of Particles

Two particles...

Question

Two particles one of mass $1$ kg and the other of mass $2$ kg are projected simultaneously with the same speed from the top of a tower. The particle of mass $1$ kg is projected vertically upward and the particle of mass $2$ kg is projected vertically downward. The acceleration of centre of mass is :

A

\frac{g}{3}

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B

g

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C

\frac{g}{2}

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D

\frac{g}{4}

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Solution

The correct option is D $g$
Acceleration of centre of mass, $a_{C M} = \frac{m_{1} a_{2} + m_{2} a_{2}}{m_{1} + m_{2}} = \frac{g + 2 g}{1 + 2} = \frac{3 g}{3} = g$ .

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