Question

A weight $W$ is supported by two strings inclined at ${60}^{\circ }$ and ${30}^{\circ }$ to vertical. The tensions in the strings are $T_1$ and $T_2$ as shown. If these tensions have to be determined in terms of $W$ using a triangle of forces, then which of the following triangles should be drawn ?
(The blocks in equilibrium)

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

For the weight $W$ to be in equilibrium, the tension in the string attached to the weight will be equal to $W$.


Now applying equilibrium at junction of string,

$\overrightarrow{T_1}+\overrightarrow{T_2}+\overrightarrow{W}=0$

Thus, $\overrightarrow{T_1},\overrightarrow{T_2}$ and $\overrightarrow{W}$ should be arrangned on a triangle in such a way that they form a closed loop.

Also, we can see that resultant of $\overrightarrow{T_1}$ and $\overrightarrow{T_2}$ should be equal to weight $\overrightarrow{W}$.

Therefore, the correct triangle representing these forces will be,


$\therefore \left(d\right)$ is the correct option.

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: If the vector sum of three forces}\\ \overrightarrow{F_1},\overrightarrow{F_2},\overrightarrow{F_3}\text{is zero, they will occupy the}\\ \text{sides of a triangle, such that resultant}\\ \text{of any two forces will give the third force.}\end{array}$