Question

A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two point masses 'm' and 2m moving in the same horizontal plane with speeds 2v and v respectively strike at the bar as shown in the Fig. and stick to the bar after collision. Calculate (a) Velocity of the centre of mass, (b) angular velocity about center of mass, and (c) total K.E. just after collision.

Answer 1

(a) Let V be the velocity of centre of mass. As no external force is applied, liner momentum is conserved.

Thus (8m + m +2m) x V = 2m (-v) + m (2v)+ 0

⇒ V = 0

(b) As no external torque is appplied, angular momentum of the system is also conserved.

(c) As the system has only rotational motion.

The total K.E. = K.E. of roration