A ball of mass ‘m’ moving with a speed 2v strikes a heavy wall elastically, which is moving with a velocity ‘v’. The work done by the heavy wall on the ball is

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$2 m v^{2}$

$\frac{1}{2} {m v^{2}}^{2}$

$m v^{2}$

None

answer is C.

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Detailed Solution

$u_{1} = 2 v, u_{2} = v, v_{1} = ?, v_{2} = v$

$v_{1} = [\frac{m_{1} - m_{2}}{m_{1} + m_{2}}] u_{1} + \frac{2 m_{2} u_{2}}{m_{1} + m_{2}}$

$\Rightarrow v_{1} = 0 [∵ m_{1} is zero compared to m_{2}]$

Workdone by wall $= - ΔK . E$ of the ball

$\Rightarrow W = - (O - 1 / 2 m (2 v)^{2}) \Rightarrow W = 2 {mv}^{2}$

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