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Question

A smooth sphere of mass $$m$$ is moving on a horizontal plane with a velocity $$3\hat{i}\, +\, \hat{j}$$. It collides with a vertical wall which is parallel to the vector $$\hat{j}$$. If the coefficient of restitution between the sphere and the wall is $$\displaystyle \frac{1}{2}$$, find the loss in kinetic energy caused by the impact.


A
278m
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B
827m
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C
278m
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D
827m
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Solution

The correct option is A $$\dfrac{27}{8}m$$
Initial velocity is $$3\hat{i}+\hat{j}$$, its magnitude is $$\sqrt10$$.
As vertical wall is along $$\hat{j}$$, the impact act on horizontal velocity, so final velocity is $$-3\hat{i}/2 + \hat{j}$$. Its magnitude is $$\sqrt{13/4}$$.
Loss in kinetic energy is $$\dfrac{1}{2}m(10-13/4)=27/8 \ m$$

Physics

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