2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{36cced0d-f982-4534-a3fe-13c32fb37f5b-04_538_625_251_657}
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\caption{Figure 1}
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A uniform lamina is in the shape of a trapezium \(A B C D\) with \(A B = a , D A = D C = 2 a\) and angle \(B A D =\) angle \(A D C = 90 ^ { \circ }\), as shown in Figure 1.
The centre of mass of the lamina is at the point \(G\).
- Show that the distance of \(G\) from \(A B\) is \(\frac { 10 a } { 9 }\).
- Find the distance of \(G\) from \(A D\).
The mass of the lamina is \(3 M\). A particle of mass \(k M\) is now attached to the lamina at \(B\). The lamina is freely suspended from the midpoint of \(A D\) and hangs in equilibrium with \(A D\) horizontal.
- Find the value of \(k\).