Physics - NLM Question with Solution | TestHub

Let $T_1$ be the tension in the upper string and $T_2,T_3$ in the strings at the lower knot. Lower knot: $T_2\cos 45^{\circ }=T_3\cos 45^{\circ }$ and $T_2\sin 45^{\circ }+T_3\sin 45^{\circ }=Mg\Rightarrow T_2=T_3=\frac{Mg}{\sqrt{2}}$.

Upper knot, horizontal: $T_1\cos \theta =T_2\cos 45^{\circ }=\frac{Mg}{2}$.

Upper knot, vertical: $T_1\sin \theta =T_2\sin 45^{\circ }+mg=\frac{Mg}{2}+mg$.

$\tan \theta =\frac{\frac{Mg}{2}+mg}{\frac{Mg}{2}}=1+\frac{2m}{M}$.