2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f180f5f0-43c5-4365-b0d8-7284220b481e-04_784_814_260_646}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a template where
- PQUY is a uniform square lamina with sides of length \(4 a\)
- RSTU is a uniform square lamina with sides of length \(2 a\)
- VWXY is a uniform square lamina with sides of length \(2 a\)
- the three squares all lie in the same plane
- the mass per unit area of \(V W X Y\) is double the mass per unit area of \(P Q U Y\)
- the mass per unit area of \(R S T U\) is double the mass per unit area of \(P Q U Y\)
- the distance of the centre of mass of the template from \(P X\) is \(d\)
- Show that \(d = \frac { 5 } { 2 } a\)
The template is freely pivoted about \(Q\) and hangs in equilibrium with \(P Q\) at an angle of \(\theta\) to the downward vertical.
Find the value of \(\tan \theta\)
The mass of the template is \(M\)
The template is still freely pivoted about \(Q\), but it is now held in equilibrium, with \(P Q\) vertical, by a horizontal force of magnitude \(F\) which acts on the template at \(X\). The line of action of the force lies in the same plane as the template.Find \(F\) in terms of \(M\) and \(g\)