4
\includegraphics[max width=\textwidth, alt={}, center]{baea9836-ea05-442f-9e87-a2a1480dc74c-2_338_957_1482_593} A uniform rod \(B C\) of length \(2 a\) and weight \(W\) is hinged to a fixed point at \(B\). A particle of weight \(3 W\) is attached to the rod at \(C\). The system is held in equilibrium by a light elastic string of natural length \(\frac { 3 } { 5 } a\) in the same vertical plane as the rod. One end of the elastic string is attached to the rod at \(C\) and the other end is attached to a fixed point \(A\) which is at the same horizontal level as \(B\). The rod and the string each make an angle of \(30 ^ { \circ }\) with the horizontal (see diagram). Find

1. the modulus of elasticity of the string,
2. the magnitude and direction of the force acting on the rod at \(B\).