Question

Three forces acting on a body and keeping it in equilibrium are as shown in the diagram. $T_{1}$ and $T_{2}$ are the tensions in the strings $O A$ and $O B$ and $W$ is the weight of the body, we have

• A. $W=T_{1}+T_{2}$
• B. $W=\sqrt{I_{1}^{2}+T_{2}^{2}}$
• C. $W=\frac{T_{1} T_{2}}{T_{1}+T_{2}}$
• D. $W=\sqrt{T_{1} T_{2}}$

Answer 1

Answer: (B)

$W \perp A B, T_{1} \perp O B \,\& \,E T_{2} \perp O A$
$\therefore \frac{W}{A B}=\frac{T_{1}}{O B}=\frac{T_{2}}{O A} \Rightarrow \frac{W}{20}=\frac{T_{1}}{16}=\frac{T_{2}}{12}$
$\Rightarrow T_{1}=\frac{4 W}{5} \& E T_{2}=\frac{3 W}{5}$
$T_{1}^{2}+T_{2}^{2}=\frac{16 W}{25}+\frac{9 W}{25}$