A light inextensible string of length $0.2\,\text{m}$ has one end fastened to a fixed point $A$ positioned above a smooth horizontal table. The other end carries a particle $P$ of mass $0.3\,\text{kg}$. $P$ travels in a horizontal circle on the table, with the string kept taut and inclined at an angle of $60^\circ$ to the downward vertical (see diagram).
(i)[3]
Calculate the tension in the string when the speed of $P$ is $1.2\,\text{m s}^{-1}$.
(ii)[6]
For the motion described, show that the angular speed of $P$ cannot be greater than $10\,\text{rad s}^{-1}$, and hence determine the greatest possible kinetic energy of $P$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Radial acceleration is $=\dfrac{1.2^2}{0.2\cos30}$” …