Question

A smooth hemisphere of mass M and radius R is at rest. A smooth solid sphere of mass 2M and radius R is moving with velocity $V_0$ between two horizontal smooth surfaces separated by a distance slightly greater than 2R as shown in the figure. Solid sphere collides with the hemisphere. If coefficient of restitution is 1/2, then

• A. the speed of hemisphere after collision is $V_0$
• B. the speed of solid sphere after collision is $\frac{3V_0}{4}$
• C. the loss in kinetic energy of the system is $\frac{1}{3}M{V}_0^2$
• D. the final kinetic energy of hemisphere is $\frac{1}{4}$ th the initial kinetic energy of sphere

Answer 1

The correct option is A the speed of hemisphere after collision is $V_0$

$2M{V}_0=2M{V}_1+M{V}_2$

$\frac{1}{2}=e=\frac{(V_2-V_1)}{V_0}$

Solving we get,

$V_1=\frac{V_0}{2}$

$V_2=V_0$

$K.E_{initial}.=\frac{1}{2}\times 2M{V}_0^2$

$K.E_{final}.=\frac{1}{2}\times 2M\times \frac{V_0^2}{4}+\frac{1}{2}\times M\times V_0^2$
$\Rightarrow LossinK.E.=\frac{1}{4}M{V}_0^2.$