Question

A ball of mass $1kg$ hangs in equilibrium from two strings $OA$ and $OB$ as shown in figure. The ratio of tensions in strings $OA$ and $OB$ is : (Take $g=10m{s}^{-2}$ )

• A. $\sqrt{3}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{1}{2\sqrt{3}}$

Answer 1

Answer: (C)

Forces acting on the ball are as shown in figure.
The three concurrent forces are in equilibrium
Using Lami's theorem.
$\frac{T_1}{sin150^{\circ }}=\frac{T_2}{sin120^{\circ }}=\frac{10}{sin90^{\circ }}$
$\Rightarrow \frac{T_1}{sin30^{\circ }}=\frac{T_2}{sin60^{\circ }}=\frac{10}{1}\Rightarrow \frac{T_1}{T_2}=\frac{sin30^{\circ }}{sin60^{\circ }}=\frac{1}{\sqrt{3}}$
$\therefore T_1=10sin30^{\circ }=10\times 0.5=5N$ and $T_2=10$
$sin60^{\circ }=10\times \frac{\sqrt{3}}{2}=5\sqrt{3}N$