A solid sphere of mass 2 kg is rolling on a horizontal surface. The absolute value of the work required to bring it to a complete stop is 140 J . The initial speed of the center of mass of the sphere is ______ m s ⁻¹ .

Step-by-step solution

According to the work-energy theorem, the work done to stop the rolling sphere is equal to its initial total kinetic energy. The total kinetic energy of a rolling solid sphere is the sum of its translational and rotational kinetic energies: K = 1 2 mv^2 + 1 2 I ^2 For a solid sphere, the moment of inertia is I = 2 5 mr^2 . Since it is rolling without slipping, = 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 Equating this to the work done: W = 7 10 mv^2 140 = 7 10 2 v^2 140 = 1.