question_answer

A particle of mass m is made to move with uniform speed v along the perimeter of a regular polygon of n sides, inscribed in a circle of radius a. The magnitude of impulse applied at each comer of the polygon is :

A) \[2mv\sin \frac{\pi }{n}\]  

B) \[mv\sin \frac{\pi }{n}\]

C) \[mv\sin \frac{n}{\pi }\]  

D) \[mv\sin \frac{n}{\pi }\]

Correct Answer: A

Solution :

[a] \[\vec{j}=m\left( {{{\vec{v}}}_{f}}-{{{\vec{v}}}_{i}} \right)\] \[=2mv\sin \theta /2=2mv\sin \pi /n.\]