Question

A ball of mass $1 \,kg$ hangs in equilibrium from two strings $O A$ and $O B$ as shown in figure. What are the tensions in strings $O A$ and $O B ?$ (Take $g=10 \,ms ^{-2}$ )

• A. 5 N, zero
• B. Zero, N
• C. $5 \,N , 5 \sqrt{3}\, N$
• D. $5 \sqrt{3}\, N , 5\, N$

Answer 1

Answer: (C)

Various 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}} $
$\frac{T_{1}}{\sin 30^{\circ}}=\frac{T_{2}}{\sin 60^{\circ}}=\frac{10}{1}$
$\therefore T_{1} =10 \sin 30^{\circ} $
$=10 \times 0.5=5\, N $
$T_{2} =10 \sin 60^{\circ} $
and$=10 \times \frac{\sqrt{3}}{2}=5 \sqrt{3} \,N$