A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J . The velocity of centre of mass of the sphere will be ______ m s - 1 .

Step-by-step solution

Let velocity of centre of mass of sphere be v . Total kinetic energy of solid sphere is K E = 1 2 m v 2 + 1 2 I ω 2 , where, I is moment of inertia of the solid sphere about the axis passing through it's centre of mass and ω = v R   pure rolling condition . Therefore, 2240 = 1 2 2 ( v ) 2 + 1 2 2 5 ( 2 ) R 2 v R 2 ⇒ 2240 = v 2 + 2 5 v 2 ⇒ v = 40   m   s - 1 .