A solid right circular cylinder is attached to a solid hemisphere of equal base. Find the ratio of the height of the cylinder to the radius of the base so that the combined centre of gravity may be at the centre of the base.

Calculate the magnitude of the smaller force if two forces act at an angle of 120° and the larger force has a magnitude of 40 N. (Note: The resultant of these two forces is perpendicular to the smaller force.)

The resultant of two like parallel forces P and Q passes through a point O. The resultant still passes through O when P and Q are increased by R and S respectively, as well as when P and Q are replaced by Q and R respectively. The force S is equal to: