Question

Find the values of tensions T1 & T2 as shown in fig. T₁ is the tension in the left inclined string and T2 is the tension in right inclined string.

Answer 1

T₁ = 100√3 N, T₂ = 100 N

Answer 2

The junction point is in equilibrium. Resolving forces horizontally and vertically:

Horizontal equilibrium: $T_2 \cos(30^\circ) - T_1 \cos(60^\circ) = 0$ $T_2 \frac{\sqrt{3}}{2} = T_1 \frac{1}{2} \implies T_1 = \sqrt{3} T_2$

Vertical equilibrium: $T_1 \sin(60^\circ) + T_2 \sin(30^\circ) - 200 = 0$ $T_1 \frac{\sqrt{3}}{2} + T_2 \frac{1}{2} = 200$

Substituting $T_1 = \sqrt{3} T_2$: $(\sqrt{3} T_2) \frac{\sqrt{3}}{2} + T_2 \frac{1}{2} = 200$ $\frac{3}{2} T_2 + \frac{1}{2} T_2 = 200 \implies 2 T_2 = 200 \implies T_2 = 100$ N

$T_1 = \sqrt{3} \times 100 = 100\sqrt{3}$ N