Probability — practice question

One end of a light inextensible string of length $0.4\,\text{m}$ is fixed to the lowest point of a hemisphere of radius $0.4\,\text{m}$, with the hemisphere’s axis vertical. A particle $P$ of mass $0.3\,\text{kg}$ is fastened to the other end of the string. The string is taut and is inclined at an angle of $30^\circ$ to the horizontal. $P$ travels on the smooth inner surface of the hemisphere in a horizontal circle (see diagram).