3
\includegraphics[max width=\textwidth, alt={}, center]{ae5d1e27-5853-48aa-9046-86ce1c1a154a-3_437_846_274_651} A block of mass 50 kg is in equilibrium on smooth horizontal ground with one end of a light wire attached to its upper surface. The other end of the wire is attached to an object of mass mkg . The wire passes over a small smooth pulley, and the object hangs vertically below the pulley. The part of the wire between the block and the pulley makes an angle of \(72 ^ { \circ }\) with the horizontal. A horizontal force of magnitude X N acts on the block in the vertical plane containing the wire (see diagram). The tension in the wire is T N and the contact force exerted by the ground on the block is R N.

1. By resolving forces on the block vertically, find a relationship between T and R . It is given that the block is on the point of lifting off the ground.
2. Show that \(\mathrm { T } = 515\), correct to 3 significant figures, and hence find the value of m .
3. By resolving forces on the block horizontally, write down a relationship between T and X , and hence find the value of \(X\).