Question

A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed v collides elastically with the stick as shown in figure.
If after the collision the ball comes to rest, then what should be the mass of the ball?

• A. m = 2M
• B. m = M
• C. m = M/2
• D. m = M/4

Answer 1

The correct option is D m = M/4

Applying law of conservation of momentum
$mv=MV$ ...(i)
Conservation of angular momentum
$mv\left(\frac{L}{2}\right)=\left(\frac{m{L}^2}{12}\right)\omega$ ...(ii)
As collision is elastic, we have
$\frac{1}{2}m{v}^2=\frac{1}{2}M{V}^2+\frac{1}{2}l{\omega }^2$ ...(iii)
Substituting the values, we get
$m=M/4$