A particle of mass 10 g moves along a circle of the radius 1 π cm with a constant tangential acceleration. What is the magnitude of this acceleration (in m s - 1 ) if the kinetic energy of the particle becomes equal to 8 × 10 - 4 J by the end of the second revolution after the beginning of the motion? (Particle starts from rest)

Step-by-step solution

Tangential acceleration a t = r α = constant = K α = K r At the end of the second revolution, angular velocity is ω then ω 2 - ω 0 2 = 2 α θ ω 2 - 0 2 = 2 K r 4 π ω 2 = 8 π K r K.E. of the particle is = K . E . = 1 2 m v 2 K . E . = 1 2 m r 2 ω 2 K . E . = 1 2 m r 2 8 π K r 8 × 10 - 4 = 1 2 × 10 - 4 × 8 × 1 π × π × K ⇒   K = 2   m   s - 2