(i)[4]
Calculate the greatest possible speed of $P$ so that the elastic string remains unextended.
(ii)[5]
Find the distance $HP$ when the angular speed of $P$ is $8\,\text{rad s}^{-1}$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
Particle $P$ has mass $0.2\,\text{kg}$ and is fastened to one end of a light inextensible string of length $0.6\,\text{m}$. At the other end, the string is joined to a particle $Q$ of mass $0.3\,\text{kg}$. It then passes through a small hole $H$ in a smooth horizontal surface. A light elastic string with natural length $0.3\,\text{m}$ and modulus of elasticity $15\,\text{N}$ connects $Q$ to a fixed point $A$, which lies $0.4\,\text{m}$ vertically below $H$. Particle $P$ travels on the surface in a horizontal circle centred at $H$ (see diagram).