7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ffe0bc72-3136-48d9-9d5b-4a364d134070-11_581_641_262_678}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
A particle of mass \(m\) is attached to one end of a light rod of length \(l\). The other end of the rod is attached to a fixed point \(O\). The rod can turn freely in a vertical plane about a horizontal axis through \(O\). The particle is projected with speed \(u\) from a point \(A\), where \(O A\) makes an angle \(\alpha\) with the upward vertical through \(O\), as shown in Figure 4. The particle moves in complete vertical circles.
Given that \(\cos \alpha = \frac { 4 } { 5 }\)
- show that \(u > \sqrt { \frac { 2 g l } { 5 } }\)
As the rod rotates, the least tension in the rod is \(T\) and the greatest tension is \(4 T\).
- Show that \(u = \sqrt { \frac { 17 } { 5 } g l }\)
\includegraphics[max width=\textwidth, alt={}]{ffe0bc72-3136-48d9-9d5b-4a364d134070-12_2639_1830_121_121}