A light pair of equal-length inextensible strings fastens a small ball $B$ of mass $0.4\ \text{kg}$ to fixed points $P$ and $Q$ on a vertical axis. Each string is taut, and both make an angle of $30^{\circ}$ with the vertical. The ball moves in a horizontal circle (see diagram).
(i)[4]
It is given that, when the ball moves at speed $6\ \text{m s}^{-1}$, the tension in string $QB$ is three times the tension in string $PB$. Calculate the radius of the circle.
(ii)[4]
The ball now travels around this circular path at the smallest possible speed. State the tension in string $PB$ in this situation, and determine the speed of the ball.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Balances the forces vertically to get $3T\cos30 - T\cos30 = 0.4g$” …