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 $\frac{1}{2}$, find the loss in kinetic energy caused by the impact.

• A. $\frac{27}{8}m$
• B. $\frac{8}{27}m$
• C. $-\frac{27}{8}m$
• D. $-\frac{8}{27}m$

Answer 1

The correct option is A $\frac{27}{8}m$

Initial velocity is $3\hat{i}+\hat{j}$, its magnitude is $\sqrt{1}0$.

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 $\frac{1}{2}m(10-13/4)=27/8m$