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…

Question

A uniform disc of mass 0 . 5 &#160; kg and radius r is projected with velocity 18 &#160; m &#160; s - 1 at t = 0 &#160; s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 &#160; s . After 2 &#160; s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 &#160; s will be ______ J . (given, coefficient of friction is 0 . 3 and g = 10 &#160; m &#160; s - 2 ).

Aicharya · Accepted Answer

Acceleration of the disc, a = - &#956; k g = - 3 &#160; m &#160; s - 2 . Now, velocity of the centre of mass v = u + a t = 18 - 3 &#215; 2 &#8658; v = 12 &#160; m &#160; s - 1 Now total kinetic energy during pure rolling( v = &#969; r ) will become, K E = 1 2 m v 2 + 1 2 I &#969; 2 = 1 2 m v 2 + 1 2 m r 2 2 v 2 r 2 &#8658; K E = 3 4 m v 2 = 3 &#215; 18 = 54 &#160; J

A uniform disc of mass 0 . 5   kg and radius r is projected with velocity 18   m   s - 1 at t…

Solution

A uniform disc of mass 0 . 5 &#160; kg and radius r is projected with velocity 18 &#160; m &#160; s - 1 at t…

Solution

A uniform disc of mass 0 . 5 kg and radius r is projected with velocity 18 m s - 1 at t…