A horizontal force F = 14 N acts at the centre of mass of a sphere of mass m = 1 kg. If the sphere rolls without sliding, find the frictional force (in N).

FBD: The forces acting on the body are F→,mg↓ and N↑ and let us assume that f is backward (←). Force equation:         F−f=ma               ...(i)N−mg=0               ...(ii)Torque equation:         f⋅R=25mR2α             ...(iii)Condition for rolling a=Rα           …(iv)Putting a from equation (i), a from equation (ii) in equation (iv), we have         F−fm=R⋅5f2mR⇒f=27F=4N