A tangential force acting on the top of sphere of mass m kept on a rough horizontal place as shown in figure. If the sphere rolls without slipping, then the acceleration with which the centre of sphere moves, is

Step-by-step solution

Let a be the acceleration of centre of sphere. The angular acceleration about the centre of the sphere is = a r , as there is no slipping. For the linear motion of the centre f+F=m a ...(i) and for the rotational motion about the centre F r-f r=I = ( 2 5 m r^2 ) ( a r ) F-f= 2 5 m a ...(ii) From Eqs. (i) and (ii) 2 F= 7 5 m a a= 10 F 7 m