5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{631b78c4-2763-4a1e-9d30-2f301fe3af2e-12_535_674_283_699}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
A particle \(P\) of mass \(m\) is attached to one end of a light inextensible string of length \(\mathrm { a } \sqrt { 3 }\). The other end of the string is attached to a fixed point A . The particle P is also attached to one end of a second light inextensible string of length a. The other end of this string is attached to a fixed point B , where B is vertically below A , with \(\mathrm { AB } = \mathrm { a }\).
The particle \(P\) moves in a horizontal circle with centre 0 , where 0 is vertically below \(B\).
The particle P moves with constant angular speed \(\omega\), with both strings taut, as shown in Figure 5.
- Show that the upper string makes an angle of \(30 ^ { \circ }\) with the downward vertical and the lower string makes an angle of \(60 ^ { \circ }\) with the downward vertical.
- Show that the tension in the upper string is \(\frac { 1 } { 2 } m \sqrt { 3 } \left( 2 g - a \omega ^ { 2 } \right)\).
- Show that \(\frac { 2 g } { 3 a } < \omega ^ { 2 } < \frac { 2 g } { a }\)
\(\_\_\_\_\) VIAV SIHI NI JIIHM ION OC
VILU SIHIL NI GLIUM ION OC
VEYV SIHI NI III HM ION OC