4. \(A B\) is a light rod. Forces \(\mathbf { F } , \mathbf { G }\) and \(\mathbf { H }\), of magnitudes \(3 \mathrm {~N} , 2 \mathrm {~N}\) and 6 N respectively, act upwards at right angles to the rod in a vertical plane at points dividing
\includegraphics[max width=\textwidth, alt={}, center]{977c24cc-8280-4881-8a62-65b7efd336ac-1_186_586_1741_1329}
\(A B\) in the ratio \(1 : 4 : 2 : 4\), as shown.
A single force \(\mathbf { P }\) is applied downwards at the point \(C\) to keep the rod horizontal in equilibrium.

1. State the magnitude of \(\mathbf { P }\).
2. Show that \(A C : C B = 5 : 6\). Two particles, of weights 3 N and \(k \mathrm {~N}\), are now placed on the rod at \(A\) and \(B\) respectively, while the same upward forces \(\mathbf { F } , \mathbf { G }\) and \(\mathbf { H }\) act as before. It is found that a single downward force at the same point \(C\) as before keeps \(A B\) horizontal under gravity.
3. Find the value of \(k\). \section*{MECHANICS 1 (A) TEST PAPER 4 Page 2}