Question

A mass m is suspended from a rigid support P by means of a massless string as shown in 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 the tension T, force F and angle θ is P

Options

• F = T sin θ

• F = T cos θ

• F = `T/(sin θ)`

• F = `T/(cos θ)`

Answer 1

F = T sin θ

Explanation:

The mass is in equilibrium at point O due to the action of the concurrent forces F, T, and W = mg. The horizontal component T sin θ must balance the force F, and the vertical component T cos θ must balance with weight W = mg. As a result, F = T sin θ.