Turn over 3 Question 1 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 1 is 6 marks) 4 2. A B P 3a a Figure 2 A small smooth ring P, of mass m, is threaded onto a light inextensible string of length 4a. One end of the string is attached to a fixed point A on a smooth horizontal table. The other end of the string is attached to a fixed point B which is vertically above A. The ring moves in a horizontal circle with centre A and radius a, as shown in Figure 2. The ring moves with constant angular speed 2 3 g a about AB. The string remains taut throughout the motion. (a) Find, in terms of m and g, the magnitude of the normal reaction between P and the table. (6) The angular speed of P is now gradually increased. (b) Find, in terms of a and g, the angular speed of P at the instant when it loses contact with the table. (3) (c) Explain how you have used the fact that P is smooth. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________