A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10 - 3 J . The speed of the centre of mass of the sphere is ______ cm 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, 7 × 10 - 3 = 1 2 × 1 × ( v ) 2 + 1 2 2 5 ( 1 ) R 2 v R 2 ⇒ 1 2 v 2 7 5 = 7 × 10 - 3 ⇒ v 2 = 10 - 2 ⇒ v = 10 - 1 = 0 . 1   m   s - 1 = 10   cm   s - 1