A bead $B$ with a smooth surface and mass $0.3\text{ kg}$ is threaded onto a light inextensible string of length $0.9\text{ m}$. One end of the string is fastened to a fixed point $A$, while the other end is fastened to a fixed point $C$ directly beneath $A$. The string has tension $T\text{ N}$, and the bead moves with angular speed $\omega\text{ rad s}^{-1}$ in a horizontal circle about the vertical axis through $A$ and $C$.
(i)[5]
As $B$ travels in a circle centred at $C$ with radius $0.2\text{ m}$, Calculate $\omega$, and then determine the kinetic energy of $B$.
(ii)[6]
If instead angle $ABC = 90^\circ$, and $AB$ makes an angle $\tan^{-1}\left(\frac{1}{2}\right)$ with the vertical, Calculate $T$ and $\omega$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Determines $\theta = \sin^{-1}(0.2/0.7) = 16.6^\circ$ with the vertical” …