2
\includegraphics[max width=\textwidth, alt={}, center]{308cecda-3bc2-4113-b7dd-ed317c5f32c5-03_638_554_260_792} The diagram shows a smooth ring \(R\), of mass \(m \mathrm {~kg}\), threaded on a light inextensible string. A horizontal force of magnitude 2 N acts on \(R\). The ends of the string are attached to fixed points \(A\) and \(B\) on a vertical wall. The part \(A R\) of the string makes an angle of \(30 ^ { \circ }\) with the vertical, the part \(B R\) makes an angle of \(40 ^ { \circ }\) with the vertical and the string is taut. The ring is in equilibrium. Find the tension in the string and find the value of \(m\).
\includegraphics[max width=\textwidth, alt={}, center]{308cecda-3bc2-4113-b7dd-ed317c5f32c5-04_521_707_259_719} A block of mass 10 kg is at rest on a rough plane inclined at an angle of \(30 ^ { \circ }\) to the horizontal. A force of 120 N is applied to the block at an angle of \(20 ^ { \circ }\) above a line of greatest slope (see diagram). There is a force resisting the motion of the block and 200 J of work is done against this force when the block has moved a distance of 5 m up the plane from rest. Find the speed of the block when it has moved a distance of 5 m up the plane from rest.