Question

A body weighing $13\, kg$ is suspended by two strings 5 m and $12 \,m$ long, their other ends being fastened to the extremities of a rod $13\, m$ long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

• A. $12\, kg$ and $13\, kg$
• B. $5\, kg$ and $5\, kg$
• C. $5 \,kg $ and $12 \,kg$
• D. $5 \,kg$ and $13\, kg$

Answer 1

The Correct Option is C

$T_{2}\,cos\left(\frac{\pi}{2}-\theta\right)=T_{1}\,cos\,\theta \Rightarrow T_{1}\,cos\,\theta =T_{2}\,sin\,\theta$ $T_{1}\,sin\,\theta+T_{2}\,cos\,\theta =13$. $\because OC=CA=CB$ $\Rightarrow ?AOC=?OAC$ and$?COB=?OBC$ $\therefore sin\theta=sinA=\frac{5}{13}$ and $cos\theta=\frac{12}{13}$ $\Rightarrow \frac{T_{1}}{T_{2}}=\frac{5}{12} \Rightarrow T_{1}=\frac{5}{12}T_{2}$ $T_{2}\left(\frac{5}{12}\cdot\frac{5}{13}+\frac{12}{13}\right)=13$ $T_{2}\left(\frac{169}{12.13}\right)=13$ $T_{2}=12\,kgs. \Rightarrow T_{1}=5\,kgs.$