A particle of mass m moving in a circular path of constant radius r such that its centripetal acceleration a_(c) is varying with time t as a_(c)= k^(2)rt^(2), where k is a constant.

A particle of mass m moving in a circular path of constant radius r su

1.	A particle of mass m moving in a circular path of constant radius r such that its centripetal acceleration a_(c) is varying with time t as a_(c)= k^(2)rt^(2), where k is a constant.
Answer» Solution :As `a_(c )=(V^(2)//R)` so `(v^(2)//r)=k^(2)rt^(2)` KINETIC energy K `= (1)/(2)mv^(2)=(1)/(2)mk^(2)r^(2)t^(2)` Now by work - Energy Theorem `W=Delta K = (1)/(2)mk^(2)r^(2)t^(2)-0rArr P =(dW)/(dt)` `RARR P=(d)/(dt)=(1)/(2)mk^(2)r^(2)t^(2)=mk^(2)r^(2)t`