Question

A rigid ball of weight 100 N suspended with the help of a string. The ball is pulled by a horizontal force F such that the string makes an angle of ${30}^{\circ }$ with the vertical. The magnitude of force F(in N)is

Answer 1

Method I:

Applying Lami's theorem
$\frac{100}{\sin {120}^{\circ }}=\frac{F}{\sin ({60}^{\circ }+{90}^{\circ })}=\frac{T}{\sin {90}^{\circ }}$
$F=\frac{100\sin {150}^{\circ }}{\sin {120}^{\circ }}=57.74N$
Method II:

This problem can be solved without applying Lami's theorem,

As,
$\therefore \theta ={30}^{\circ },then$
Vertical reactions,
$T\cos {30}^{\circ }=100N$
$T=\frac{100\times 2}{\sqrt{3}}N=\frac{200}{\sqrt{3}}$
Horizontal reactions,
$F=T\cos {60}^{\circ }$
$=\frac{200}{\sqrt{3}}\times \frac{1}{2}=\frac{100}{\sqrt{3}}=57.74N$