A particle of mass m is moving in a horizontal circle of radius R under a centripetal force equal to - A R² (A= constant ) . The total energy of the particle is

Step-by-step solution

Given, centripetal force, F=- A R² Potential energy, U=- d F d R aligned &=- d d R (- A R² ) &=- A R aligned In circular motion, centripetal force is responsible for the motion of object. aligned & m v² R = A R² & m v²= A R & 1 2 m v²= A 2 R & Kinetic energy, K= 1 2 m v²= A 2 R & Total energy =U+K =- A R + A 2 R =- A 2 R aligned