JEE Main · 2007 · 29 Apr 2007 · Offline · Chapter_pending

The two strings of lengths $5$ and $12$ together with the $13$-long rod make a right angle at the hanging weight, because $5^2+12^2=13^2$. Writing $\sin \theta =\frac{5}{13}$ and $\cos \theta =\frac{12}{13}$ for the geometry, horizontal balance gives $\frac{12}{13}{T}_1=\frac{5}{13}{T}_2$ and vertical balance gives $\frac{5}{13}{T}_1+\frac{12}{13}{T}_2=13$. Solving the pair together gives string tensions of $5$ kg and $12$ kg.