Question

A body of mass $5\text{kg}$ is suspended by the strings making angles ${60}^o$ and ${30}^o$ with the horizontal as shown in the figure. Find the tension in the strings. ($g=10{\text{m/s}}^2$ )

• A. $T_1=25\text{N}$ & $T_2=25\text{N}$
• B. $T_1=25\sqrt{3}\text{N}$ & $T_2=25\text{N}$
• C. $T_1=25\text{N}$ & $T_2=25\sqrt{3}\text{N}$
• D. $T_1=25\sqrt{3}\text{N}$ & $T_2=25\sqrt{3}\text{N}$

Answer 1

The correct option is C $T_1=25\text{N}$ & $T_2=25\sqrt{3}\text{N}$



Taking components of both $T_1$ and $T_2$ along horizontal and vertical direction, we get

For horizontal equilibrium of mass $5\text{kg}$: $\begin{array}{}{T}_2\cos {60}^o=T_1\cos {30}^o& \text{(i)}\end{array}$
For vertical equilibrium of mass $5\text{kg}$
$\begin{array}{}{T}_2\sin {60}^o+T_1\sin {30}^o=5g& \text{(ii)}\end{array}$
From equations (i) and (ii)
$T_1=25\text{N}$ and $T_2=25\surd 3\text{N}$