A smooth solid hemisphere has its flat surface lying on a horizontal table and its curved surface facing upwards. The flat face of the hemisphere has centre and radius . Point , at which a particle is placed, is the highest point on the hemisphere. is then given an initial horizontal speed , where and the acceleration due to gravity is . Find the angle between the velocity of and the table as strikes the table, giving your answer to the nearest degree.
A bead of mass 0.6 kg is attached to one end of a light rod of length 0.9 m. The other end of the rod is fixed at a point , about which the rod can freely rotate in a vertical plane. The rod is held at an angle of to the upward vertical and released from rest. Taking , find the tension in the rod as it passes the horizontal. Give your answer in newtons, correct to one decimal place.