Two particles \( P \) and \( Q \) of masses \( 0.5 kg \) and \( m kg \) respectively are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the top of two inclined planes. The particles are initially at rest with \( P \) on a smocth plane inclined at \( 30^{\circ} \) to the horizontal and \( Q \) on a plane inclined at \( 45^{\circ} \) to the horizontal. The string is taut and the particles can move on lines of greatest slope of the two planes. A force of magnitude \( 0.8 N \) is applied to \( P \) acting down the plane, causing \( P \) to move down the plane (see diagram). (a) It is given that \( m=0.3 \), and that the plane on which \( Q \) rests is smooth. Find the tension in the string. [5]

Question

Two particles \( P \) and \( Q \) of masses \( 0.5 kg \) and \( m kg \) respectively are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the top of two inclined planes. The particles are initially at rest with \( P \) on a smocth plane inclined at \( 30^{\circ} \) to the horizontal and \( Q \) on a plane inclined at \( 45^{\circ} \) to the horizontal. The string is taut and the particles can move on lines of greatest slope of the two planes. A force of magnitude \( 0.8 N \) is applied to \( P \) acting down the plane, causing \( P \) to move down the plane (see diagram). (a) It is given that \( m=0.3 \), and that the plane on which \( Q \) rests is smooth. Find the tension in the string.