A uniform disc of mass 0 . 5 kg and radius r is projected with velocity 18 m s - 1 at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s . After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be ______ J . (given, coefficient of friction is 0 . 3 and g = 10 m s - 2 ).

Step-by-step solution

Acceleration of the disc, a = - μ k g = - 3   m   s - 2 . Now, velocity of the centre of mass v = u + a t = 18 - 3 × 2 ⇒ v = 12   m   s - 1 Now total kinetic energy during pure rolling( v = ω r ) will become, K E = 1 2 m v 2 + 1 2 I ω 2 = 1 2 m v 2 + 1 2 m r 2 2 v 2 r 2 ⇒ K E = 3 4 m v 2 = 3 × 18 = 54   J