Moments

A heavy uniform sphere of radius a has a light inextensible string attached to a point on its surface. The other end of the string is fixed to a point on a rough vertical wall. The sphere rests in equilibrium touching the wall at a point distant h below the fixed point.

If the point of the sphere in contact with the wall is about to slip downwards and the coefficient of friction between the sphere and the wall is μ find the inclination of the string to the vertical.

If μ=h/(2a) and the weight of the sphere is W, show that the tension in the string is (1+μ2)1/22μW