2
\includegraphics[max width=\textwidth, alt={}, center]{76a47bf6-1982-4cdb-bcaa-2cdf84cc4f37-2_515_463_484_842} A uniform wire has the shape of a semicircular arc, with diameter \(A B\) of length 0.8 m . The wire is attached to a vertical wall by a smooth hinge at \(A\). The wire is held in equilibrium with \(A B\) inclined at \(70 ^ { \circ }\) to the upward vertical by a light string attached to \(B\). The other end of the string is attached to the point \(C\) on the wall 0.8 m vertically above \(A\). The tension in the string is 15 N (see diagram).

1. Show that the horizontal distance of the centre of mass of the wire from the wall is 0.463 m , correct to 3 significant figures.
2. Calculate the weight of the wire.