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 center of mass of the sphere in cm s ⁻¹ is

Step-by-step solution

Total kinetic energy of a solid sphere rolling without slipping is the sum of its translational and rotational kinetic energies. K = 1 2 mv^2 + 1 2 I ^2 For a solid sphere, I = 2 5 mr^2 and for pure rolling, = v r . K = 1 2 mv^2 + 1 2 ( 2 5 mr^2 ) ( v r )^2 K = 1 2 mv^2 + 1 5 mv^2 = 7 10 mv^2 Given K = 7 10⁻³ J and m = 1 kg. 7 10⁻³ = 7 10 1 v^2 v^2 = 10⁻² v = 0.1 m s ⁻¹ v = 10 cm s ⁻¹ Answer: 10