9709/Oct Nov/43/2011/Q6

The diagram shows a ring of mass 2 kg threaded on a fixed rough vertical rod. A light string is attached to the ring and is pulled upwards at an angle of 30◦ to the horizontal. The tension in the string is T N. The coefficient of friction between the ring and the rod is 0.24. Find the two values of T for which the ring is in limiting equilibrium. 

Solution:

Reference: PYQ - Oct/Nov 2011 Paper 43 Q6

9709/May June/2011/42/Q6

A small smooth ring R, of mass 0.6 kg, is threaded on a light inextensible string of length 100 cm. One end of the string is attached to a fixed point A. A small bead B of mass 0.4 kg is attached to the other end of the string, and is threaded on a fixed rough horizontal rod which passes through A. The system is in equilibrium with B at a distance of 80 cm from A (see diagram).

(i) Find the tension in the string. 

(ii) Find the frictional and normal components of the contact force acting on B. 

(iii) Given that the equilibrium is limiting, find the coefficient of friction between the bead and the rod.

Solution:

Reference: PYQ - May/Jun 2011 Paper 42 Q6

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

9709/Oct Nov/2002/4/Q3

A light inextensible string has its ends attached to two fixed points A and B, with A vertically above B. A smooth ring R, of mass 0.8 kg, is threaded on the string and is pulled by a horizontal force of magnitude X newtons. The sections AR and BR of the string make angles of 50^o and 20^o  respectively with the horizontal, as shown in the diagram. The ring rests in equilibrium with the string taut. Find

(i) the tension in the string,

(ii) the value of X.

Solution:

Reference: PYQ - Oct/Nov 2002 Paper 4 Q3