Question

Calculate the tensions $T_1,T_{2}and{T}_3$ in the three threads shown in the following figure. (All threads are massless) $\left(g=10m/s^2\right)$

• A. $30N,40N,50N$
• B. $50N,30N,40N$
• C. $35N,45N,40N$
• D. $30N,50N,40N$

Answer 1

The correct option is D $30N,50N,40N$

Tension $T_3=mg=4\times 10=40N$

Apply lami’s theorem

$\frac{T_1}{\sin \alpha }=\frac{T_2}{\sin \beta }=\frac{T_3}{\sin \gamma }$

$\frac{T_1}{\sin \left({143}^o\right)}=\frac{T_2}{\sin \left({90}^o\right)}=\frac{40}{\sin \left({127}^o\right)}$

$T_1=\frac{40\sin \left({143}^o\right)}{\sin \left({127}^o\right)}=30N$

$T_2=\frac{40\sin \left({90}^o\right)}{\sin \left({127}^o\right)}=50N$

Tension, $T_1,T_{2}and{T}_{3}is30N,50Nand40N$