Question

Find the ratio of the tension $T_1$ and $T_2$ in the string as shown in the figure. Take $g=10{\text{m/s}}^2$.

• A. $4$
• B. $1.5$
• C. $1$
• D. $2$

Answer 1

The correct option is D $2$

Mass of block, $m=8\text{kg}$
Resolving the tension $T_1$ along horizontal ($x$) and vertical direction ($y$).


Applying the condition of equilibrium on the block in $x$ and $y$ direction
$\sum F_x=0$
$\Rightarrow T_2=T_1\cos {60}^{\circ }...\left(1\right)$
$\Rightarrow \frac{T_2}{T_1}=\frac{1}{2}$
$\therefore \frac{T_1}{T_2}=2$

ALTERNATIVE:

$\sum F_y=0$
$\Rightarrow T_1\sin {60}^{\circ }=80\text{N}...\left(2\right)$
$\Rightarrow T_1=\frac{160}{\sqrt{3}}$
$\Rightarrow T_2=T_1\cos {60}^{\circ }=\frac{80}{\sqrt{3}}$
$\therefore \frac{T_1}{T_2}=2$