Question

A box of weight $10\sqrt{3}$ N is held in equilibrium with the help of two strings OA and OB as shown in figure-I. The string OA is horizontal. Find the tensions in both the strings.

Answer 1

For equilibrium horizontal force must be balanced.

$T_1\sin \theta =T_2\cos 60°\to \left(1\right)$

$T_1\cos \theta =T_2\sin 60=10\sqrt{3}\to \left(1\right)$

$T_1\cos \theta +\frac{2T_1\sin \theta \times \sqrt{3}}{2}=10\sqrt{3}$

$T_1[\cos \theta +\sqrt{3}\sin \theta ]=10\sqrt{3}$

$T_1=\frac{10\sqrt{3}}{\cos \theta +\sqrt{3}\sin \theta }$

$T_2=2T_1\sin 60$

$T_2=\frac{30}{\cos \theta +\sqrt{3}\sin \theta }$