Mathematics 9709/43 — October/November 2015

A small ball $B$ of mass $4\text{ kg}$ is attached to one end of a light inextensible string. A particle $P$ of mass $3\text{ kg}$ is attached to the other end of the string. The string passes over a fixed smooth pulley. The system is in equilibrium with the string taut and its straight parts vertical. $B$ is at rest on a rough plane inclined to the horizontal at an angle of $\alpha$, where $\cos \alpha = 0.8$ (see diagram). State the tension in the string and find the normal component of the contact force exerted on $B$ by the plane.