Question

A ball of mass $1kg$ hangs in equilibrium from two strings OA and OB as shown in figure. What are the tensions in strings OA and OB? (Take $g=10m/s^2$).

Answer 1

Various forces acting on the ball are as shown in figure. The three concurrent forces are in equilibrium. Using Lami's theorem,
$\frac{T_1}{\sin {150}^{\circ }}=\frac{T_2}{\sin {120}^{\circ }}=\frac{10}{\sin {90}^{\circ }}$
or $\frac{T_1}{\sin {30}^{\circ }}=\frac{T_2}{\sin {60}^{\circ }}=\frac{10}{1}$
$\therefore T_1=10\sin {30}^{\circ }=10\times 0.5=0.5N$
and $T_2=10\sin {60}^{\circ }=10\times \frac{\sqrt{3}}{2}$
$=5\sqrt{3}N$