Question

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

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

Answer 1

The correct option is C $5\text{N},5\sqrt{3}\text{N}$

Taking the componet of $T_1$ and $T_2$ in $x$ and $y$ direction

$\sum F_y=0$
$T_1\sin {30}^0+T_2\sin {60}^0=10$
$\begin{array}{}\frac{T_1}{2}+\frac{\sqrt{3}{T}_2}{2}=10& \text{(1)}\end{array}$
$\sum F_x=0$
$T_1\cos {30}^0=T_2\cos {60}^0$
$\frac{\sqrt{3}{T}_1}{2}=\frac{T_2}{2}$
$\begin{array}{}{T}_1=\frac{T_2}{\sqrt{3}}& \text{(2)}\end{array}$
Substitute $T_1$ in equation 1
$\frac{T_2}{2\sqrt{3}}+\frac{\sqrt{3}{T}_2}{2}=10$
$T_2+3T_2=20\sqrt{3}$
$T_2=5\sqrt{3}N$
and $T_1=5N$