Question

A body of mass m is kept in equilibrium by two strings making an angle ${30}^{\circ }$ and ${45}^{\circ }$ with the horizontal as shown. The ratio of the tensions in the string is

• A. (a) 1: $\sqrt{6}$
• B. (b) $\sqrt{2}$ : 2
• C. (c) $\sqrt{2}$ : $\sqrt{3}$
• D. (d) $\sqrt{3}$ : 2

Answer 1

The correct option is D (d) $\sqrt{3}$ : 2

At equilibrium,

$T_{1}cos30=T_{2}cos45\to \left(1\right)T_{1}sin30+T_{2}sin45=mg\to \left(2\right)From\left(1\right)\frac{T_1}{T_2}=\frac{cos45}{sin30}=\frac{\frac{1}{\sqrt{2}}}{\frac{\sqrt{3}}{3}}=\frac{\sqrt{2}}{\sqrt{3}}\Rightarrow T_1{:T}_2=\sqrt{2}:\sqrt{3}$