7 Two identical light, inextensible strings \(S _ { 1 }\) and \(S _ { 2 }\) are each of length 5 m . Two identical particles \(P\) and \(Q\) are each of mass 1.5 kg .
One end of \(S _ { 1 }\) is attached to \(P\). The other end of \(S _ { 1 }\) is attached to a fixed point \(A\) on a smooth horizontal plane. \(P\) moves with constant speed in a horizontal circular path with \(A\) as its centre (see Fig. 1).
One end of \(S _ { 2 }\) is attached to \(Q\). The other end of \(S _ { 2 }\) is attached to a fixed point \(B\). \(Q\) moves with constant speed in a horizontal circular path around a point \(O\) which is vertically below \(B\). At any instant, \(B Q\) makes an angle of \(\theta\) with the downward vertical through \(B\) (see Fig. 2).
\begin{figure}[h]
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\caption{Fig. 1}
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\begin{figure}[h]
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\caption{Fig. 2}
\includegraphics[alt={},max width=\textwidth]{b190b8c9-75b0-4ede-913f-cdecdb58180f-5_471_469_932_1151}
\end{figure}
- Given that the angular speed of \(P\) is the same as the angular speed of \(Q\), show that the tensions in \(S _ { 1 }\) and \(S _ { 2 }\) have the same magnitude.
- You are given instead that the kinetic energy of \(P\) is 39.2 J and that this is the same as the kinetic energy of \(Q\).
Determine the difference between the times taken by \(P\) and \(Q\) to complete one revolution. Give your answer in an exact form.