3
\includegraphics[max width=\textwidth, alt={}, center]{b9080e9f-2c23-43ce-b171-bd68648dc56b-3_764_627_274_758}
A uniform beam \(A B\) has length 2 m and mass 10 kg . The beam is hinged at \(A\) to a fixed point on a vertical wall, and is held in a fixed position by a light inextensible string of length 2.4 m . One end of the string is attached to the beam at a point 0.7 m from \(A\). The other end of the string is attached to the wall at a point vertically above the hinge. The string is at right angles to \(A B\). The beam carries a load of weight 300 N at \(B\) (see diagram).
- Find the tension in the string.
The components of the force exerted by the hinge on the beam are \(X \mathrm {~N}\) horizontally away from the wall and \(Y \mathrm {~N}\) vertically downwards.
- Find the values of \(X\) and \(Y\).