Question

A block of weight 100 N is suspended with the help of three string ( as shown) . Find the tension in each of these strings

Answer 1

Given,

A block weight is $100N$

So, the resolution of forces along the horizontal direction gives, $T_{1}cos{30}^0=T_{2}cos{45}^0$

$T_1\times \frac{\sqrt{3}}{2}=T_2\times \frac{1}{\sqrt{2}}$

$T_2=\sqrt{\frac{3}{2}}{T}_1$

Now the resolution of the forces alog the vertical direction gives,

$T_{1}sin{30}^0+T_{2}sin{45}^0=100N$

$T_1\frac{1}{2}+\frac{\sqrt{3}}{2}{T}_1\times \frac{1}{\sqrt{2}}$

$T_1(1+\sqrt{3})=200$

$T_1=\frac{200}{2.732}=73.2N$ Since $[\sqrt{3}=1.732]$

$T_2=\frac{\sqrt{3}}{2}\times 73.2=89.65N$