A particle is moving in a circle of radius r under the action of a force F = α r 2 which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy = 0 for r = 0 ):

Step-by-step solution

Force F = α r 2 will act as centripetal force ⇒ α r 2 = m v 2 r ⇒ m v 2 = α r 3 ∴ Kinetic energy K . E . = 1 2 m v 2 ⇒ K . E . = α r 3 2 Also d U = - F → . d r → ∆ U = - ∫ F → . d r → = - ∫ α r 2 - d r = α ∫ 0 r r 2 d r U - 0 = α r 3 3 ⇒ U = α r 3 3 So total mechanical energy E = U + K = α r 3 3 + α r 3 2 E = 5 α r 3 6