3 A block of mass 3 kg is at rest on a rough plane inclined at \(60 ^ { \circ }\) to the horizontal. A force of magnitude 15 N acting up a line of greatest slope of the plane is just sufficient to prevent the block from sliding down the plane.

1. Find the coefficient of friction between the block and the plane.
   The force of magnitude 15 N is now replaced by a force of magnitude \(X \mathrm {~N}\) acting up the line of greatest slope.
2. Find the greatest value of \(X\) for which the block does not move.
   \includegraphics[max width=\textwidth, alt={}, center]{dd1828e1-5b90-4584-92de-f00f9c4f9657-06_332_967_260_589} Two blocks \(A\) and \(B\) of masses 4 kg and 5 kg respectively are joined by a light inextensible string. The blocks rest on a smooth plane inclined at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 7 } { 24 }\). The string is parallel to a line of greatest slope of the plane with \(B\) above \(A\). A force of magnitude 36 N acts on \(B\), parallel to a line of greatest slope of the plane (see diagram).