If the radius of the circular path and frequency of revolution of a particle of mass m are doubled, then the change in its kinetic energy will be ( E i and E f are the initial and final kinetic energies of the particle respectively,)

Step-by-step solution

Initial kinetic energy of body, E i = 1 2 m v 2 = 1 2 m 2 π r 1 T 1 ∵ v = 2 π r T E i = 2 π 2 m r 1 2 f 1 2 Where , f 1 = frequency of revolution of the body. When, r 2 = 2 r 1 and f 2 = 2 f 1 then E f = 2 π 2 m . r 2 2 . f 2 2 = 2 π 2 m 2 r 1 2 2 f 1 2 E f = 32 π 2 m r 1 2 f 1 2 = 16.2 π 2 m r 1 2 f 1 2 E f = 16 E i ∴ Change in kinetic energy, Δ E = E f - E i = 16 E i - E i = 15 E i