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 $g=10ms^{- 2}$ )

• 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.
$\frac{T_{1}}{sin 150 ^\circ }=\frac{T_{2}}{sin 120 ^\circ }=\frac{10}{sin 90 ^\circ }$
$\Rightarrow \frac{T_{1}}{sin 30 ^\circ }=\frac{T_{2}}{sin 60 ^\circ }=\frac{10}{1}\Rightarrow \frac{T_{1}}{ T_{2}}=\frac{sin 30 ^\circ }{sin 60 ^\circ }=\frac{1}{\sqrt{3}}$
$\therefore T_{1}=10sin30^\circ =10\times 0.5=5N$ and $T_{2}=10$
$sin60^\circ =10\times \frac{\sqrt{3}}{2}=5\sqrt{3}N$