page 08 MARKS 18. A particle of mass m kg is attached to a light inextensible string. The mass is rotating in a vertical circle of radius r metres. Its velocity at the top of the circle is 1 2 3 ms gr . (a) Find an expression in terms of g and r for the maximum velocity of the particle. On another occasion, the same string and mass are set in motion so that the mass has velocity 1 2 ms gr  at the lowest point of the circle. The angle between the string and the downward vertical is θ. (b) (i) Show that at the point where the tension in the string becomes zero, cos 2 3 θ  . (ii) Describe the motion of the particle after this point. 19. A particle of mass, m kg, is suspended in equilibrium from a point A on the ceiling of a room by a light spring of natural length l metres and modulus of elasticity 2 mg newtons. (a) Show that the extension of the spring is 2 l  metres. A second identical spring is attached to the particle and secured to a point B on the floor of the room. B is vertically below A and the distance AB is 3l metres. (b) Given that both springs remain in tension when the particle is again in equilibrium, find an expression in terms of l for the extension of the original spring. [END OF QUESTION PAPER] 3 5 1 2 4 Acknowledgement of copyright Question 1 Nerthuz/shutterstock.com