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Perfectly Elastic Collision

The pendulum ...

Question

The pendulum ball of mass $m_{1}$ is let to swing from a height $h$ . It strikes and sticks to the pendulum ball $m_{2}$ , which is at rest. The combination then swings to a height $\frac{h}{3}$ , then $m_{2}$ in terms of $m_{1}$ is

17.32 m_{1}

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1.732 m_{1}

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0.732 m_{1}

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m_{1}

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Solution

The correct option is C $0.732 m_{1}$
Velocity of $m_{1}$ before colliding $m_{2} = \sqrt{2 g h}$
using momentum conservation

$m_{1} \times \sqrt{2 g h} = (m_{1} + m_{2}) \sqrt{\frac{2 g h}{3}}$

$\sqrt{3} m_{1} = m_{1} + m_{2}$

$(\sqrt{3} - 1) m_{1} = m_{2}$

$\Rightarrow m_{2} = 0.732 m_{1}$

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