A body of weight W 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 `theta` with the vertical. If the tension in the string is T,

Options

A. F=Tsin`theta`
B. W=Tsin`theta`
C. T= `sqrt(W^2+F^2)`
D. F=W tantheta

Answer

A, C, D

Explanation

The mass in equilibrium at point O under the action of the concurrent forces F, T and W =mg.,Therefore, as shown in figure, the horizontal component T sin `theta` tension T must-balance with force F and the vertical component T cos `theta` must balance with weight W =mg. Thus `F = Tsin theta` ---------(i)
and `W = T cos theta` ---------ii)
Squaring Eqs. (i) and (ii) and adding we get `T^2=W^2+F^2`
Dividing (i) by (ii) we get `F = W tan theta`.