Mathematics 9709/41 — October/November 2013

A particle $P$ of mass $0.3\text{ kg}$ is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point $X$. A horizontal force of magnitude $F\text{ N}$ is applied to the particle, which is in equilibrium when the string is at an angle $\alpha$ to the vertical, where $\tan \alpha = \frac{8}{15}$ (see diagram). Find the tension in the string and the value of $F$.