Question

Two small particles A & B of masses M and 2M respectively are joined rigidly to the ends of a light rod of length l as shown in the figure. The system translates on a smooth horizontal surface with a velocity u in a direction perpendicular to the rod. A particle P of mass M kept at rest on the surface sticks to the particle ‘A’ after collision with it. Then choose the correct option(s):

• A. The speed of particle A just after collision is $\frac{u}{2}$ .
• B. The speed of particle B just after collision is $\frac{u}{2}$ .
• C. The velocity of centre of mass of system A + B + P is $\frac{3u}{4}$
• D. The angular velocity of the system A + B + P after collision is $\frac{u}{2l}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A

The speed of particle A just after collision is $\frac{u}{2}$ .

C

The velocity of centre of mass of system A + B + P is $\frac{3u}{4}$

D

The angular velocity of the system A + B + P after collision is $\frac{u}{2l}$

By linear momentum conversation
M(u) + M(0) = (2M)v'
$v^{\prime }=\frac{u}{2}{V}_{CM}=\frac{2M\left(u\right)+\left(2M\right)\frac{u}{2}}{4M}=\frac{3u}{4}\omega =\frac{u-\frac{u}{2}}{l}=\frac{u}{2l}$