question_answer

Two particles A and 5 each of mass m are attached by a light inextensible string of length\[2l\] The whole system lies on a smooth horizontal surface. Now particle B starts moving with velocity u as shown. The velocity of particle A when the string jerks tight is

A) \[\frac{u\sqrt{3}}{4}\]   

B) \[\frac{u}{\sqrt{3}}\]

C) \[\frac{u\sqrt{3}}{2}\]               

D) \[\frac{u}{2}\]

Correct Answer: A

Solution :

[a] When the string jerks tight both particles begin to move with velocity components v in the direction AB. Using conservation of momentum in the direction AB, \[mu\text{ }cos\text{ }30{}^\circ =mv+mv\] or      \[v=\frac{u\sqrt{3}}{4}\] Hence the velocity of ball A just after the jerk is \[\frac{u\sqrt{3}}{4}\].