A yo-yo consists of two uniform discs, each of mass M and radius R, connected by a short light axle of radius a around which a portion of a thin string is wound. One end of the string is attached to the axle and the other to a fixed point P. The yo-yo is held with its centre of mass vertically below P and then released. (a) Assuming that the unwound part of the string remains approximately vertical, use the principle of conservation of energy to find the equation of motion of the centre of mass of the yo-yo. (b) Find the tension in the string as the yoyo falls. (c) If the string has length L, what is the speed of the yoyo just before it reaches the end? Explain what happens next. What is the change in momentum (i.e. the so called impulse) due to the tension in the string at this time?