A particle of mass m is 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. What is the power delivered to the particle by the forces acting on it?

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

1.	A particle of mass m is 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. What is the power delivered to the particle by the forces acting on it?
Answer» <P> Solution :As `a_(c )= (V^(2)//r) " so" (v^(2)//r)= k^(2) r t^(2)` Kinetic energy `K= (1)/(2) mv^(2)= (1)/(2) mk^(2) r^(2) t^(2)` Now by work -Enetgy THEOREM `W= Delta K= (1)/(2) mk^(2) r^(2) t^(2)- 0 rArr P= (dw)/(dt)` `rArr P= (d)/(dt) = (1)/(2) mk^(2) r^(2) t^(2)= mk^(2) r^(2) t`