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. $m=\frac{M}{2}$
• D. $m=\frac{M}{4}$

Answer 1

The correct option is D

$m=\frac{M}{4}$

By linear momentum conservation:
Mu = mv

$u=\frac{mv}{M}$

and $\omega =\frac{(v-\frac{mv}{M})}{\frac{L}{2}}=2v\left(\frac{M-m}{NL}\right)$

by angular momentum conservation about P:

$M\left(\frac{mv}{M}\right)\frac{L}{2}=\frac{M{L}^2}{12}\left(\frac{2v(M-m)}{NL}\right)$

$\Rightarrow m=\frac{M}{4}$