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 r t 2 , where k is a constant. The power delivered to the particle by the force acting on it is

Step-by-step solution

a c = k 2 r t 2 or v 2 r = k 2 r t 2 or v = k r t Therefore, tangential acceleration, a t = d v d t = k r or Tangential force, F t = m a t = m k r Only tangential force does work. P o w e r = F t v = m k r k r t or P o w e r = m k 2 r 2 t