5 One end of a light elastic string $S _ { 1 }$ of modulus of elasticity 20 N and natural length 0.5 m is attached to a fixed point $O$. The other end of $S _ { 1 }$ is attached to a particle $P$ of mass $0.4 \mathrm {~kg} . P$ hangs in equilibrium vertically below $O$.\\
(i) Find the distance $O P$.

The opposite ends of a light inextensible string $S _ { 2 }$ of length $l \mathrm {~m}$ are now attached to $O$ and $P$ respectively. The elastic string $S _ { 1 }$ remains attached to $O$ and $P$. The particle $P$ hangs in equilibrium vertically below $O$.\\
(ii) Find the tension in the inextensible string $S _ { 2 }$ for each of the following cases:\\
(a) $l < 0.5$;\\
(b) $l > 0.6$;\\
(c) $l = 0.54$.

In the case $l = 0.54$, the inextensible string $S _ { 2 }$ suddenly breaks and $P$ begins to descend vertically.\\
(iii) Calculate the greatest speed of $P$ in the subsequent motion.

\hfill \mbox{\textit{CAIE M2 2013 Q5}}