A solid uniform hemisphere, of radius r, is placed onto a rough plane inclined at 45° to the horizontal. A force, P, parallel to and up the plane, is applied to the hemisphere at a point that is r/2 above the surface of the plane. The highest point on the rim of the hemisphere that touches the plane is denoted by A.

a. Assuming that the friction is great enough to prevent slipping, find the value of P required to make the hemisphere topple up the plane. Give your answer in terms of m and g.

b. Let µ = 3/4 and let the hemisphere be on the point of slipping up the plane. Find the distance between the reaction force and the point A.