9709/Oct Nov/2003/4/Q6

One end of a light inextensible string is attached to a fixed point A of a fixed vertical wire. The other end of the string is attached to a small ring B, of mass 0.2 kg, through which the wire passes.

A horizontal force of magnitude 5N is applied to the mid-point M of the string. The system is in equilibrium with the string taut, with B below A, and with angles ABM and BAM equal to 30◦ (see diagram).

(i) Show that the tension in BM is 5N.

(ii) The ring is on the point of sliding up the wire. Find the coefficient of friction between the ring and the wire.

(iii) A particle of mass m kg is attached to the ring. The ring is now on the point of sliding down the wire. Given that the coefficient of friction between the ring and the wire is unchanged, find the value of m.

Solution:

Reference: PYQ - Oct/Nov 2003 Paper 4 Q6