Question

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 $\theta$ with the vertical. Then the relation between tension T, force F and angle $\theta$ is

• A. $F=Tsin\theta$
• B. $F=Tcos\theta$
• C. $F=\frac{T}{sin\theta }$
• D. $F=\frac{T}{cos\theta }$

Answer 1

The correct option is A

$F=Tsin\theta$

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.
$\therefore F=Tsin\theta$ and
$W=Tcos\theta$

Thus, the correct choice is (a).