A mass m is suspended from a rigid support P by means of a massless string as shown in the figure. A horizontal force F is applied at point O of the rope. The system is in equilibrium when the string makes an angle θ with the vertical. Then the relation between tension T, force F and angle θ is
F=T sin θ
The mass m is in equilibrium at point O under the action of three concurrent forces F, T and W = mg. The horizontal component of tension T must balance the force F and the vertical component must balance weight W.
∴F=T sinθ and
W=T cosθ
Thus, the correct choice is (a).