Problem

Figure 1

Figure 1 shows a small smooth ring threaded onto a light inextensible string. One end of the string is attached to a fixed point $A$ on a horizontal ceiling and the other end of the string is attached to a fixed point $B$ on the ceiling.

A horizontal force of magnitude $2\text{ N}$ acts on the ring so that the ring rests in equilibrium at a point $C$, vertically below $B$, with the string taut.

The line of action of the horizontal force and the string both lie in the same vertical plane.

The angle that the string makes with the ceiling at $A$ is $\theta$, where $\tan \theta = \frac{3}{4}$

The tension in the string is $T$ newtons. The mass of the ring is $M\text{ kg}$.

(a) Find the value of $T$

(b) Find the value of $M$