Question

A body of weight 200 N is suspended with the help of string as shown in the figure. Find the tensions in the strings.

Answer 1

Use lomi's theorem.....

Answer 2

resolution of $T_1$ :
x - direction => $T_1cos30^{\circ}(\leftarrow)$
y- direction => $T_1sin30^{\circ}$

resolution of $T_2$ :
x - direction => $T_2cos45^{\circ}(\rightarrow)$
y- direction => $T_2sin45^{\circ}$

at equilibrium ,
$T_1cos30^{\circ}=T_2cos45^{\circ}$
$\frac{\sqrt{3}T_1}{2}=\frac{\sqrt{2}T_2}{2}$
$\sqrt{3}T_1=\sqrt{2}T_2$.....(1)

and
$T_1sin30+T_2sin45°=200N$

$0.5T_1+\frac{\sqrt{2}T_2}{2}=200N$

from equation (1),

$\frac{\sqrt{2}T_2}{2\sqrt{3}}+\frac{2T_2}{2\sqrt{2}}=200N$

T_2/√2√3 + T/√2 = 200
(√3 + 1)T_2/√6 = 200

T_2 = 200√6/(√3 + 1) N

so, T_1 = 400/(√3 + 1)