A ball moving with velocity 2 m/s collides head-on with another stationary ball of double the mass.If the coefficient of restitution is 0.5 then their velocities (in m/s) after collision will be :

0, 2

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0, 1

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1, 1

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1, 0.5

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Solution

The correct option is B 0, 1
Given : $m_{1} = m$ $u_{1} = 2 m / s$ $m_{2} = 2 m$ $u_{2} = 0$ $e = 0.5$

Velocity of mass $m_{1}$ after collision $V_{1} = \frac{(m_{1} - e m_{2}) u_{1} + (1 + e) u_{2} m_{2}}{m_{1} + m_{2}}$

$⟹$ $V_{1} = \frac{(m - 0.5 \times (2 m) 2 + (1 + 0.5) \times 0}{m + 2 m} = 0 m / s$

Velocity of mass $m_{2}$ after collision $V_{2} = \frac{(m_{2} - e m_{1}) u_{2} + (1 + e) u_{1} m_{1}}{m_{1} + m_{2}}$

$⟹$ $V_{2} = \frac{(2 m - 0.5 (m) \times 0 + (1 + 0.5) \times m \times 2}{m + 2 m} = 1 m / s$

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