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  4. The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle θ should be

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Q. The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle $\theta$ should bePhysics Question Image

IIT JEEIIT JEE 2001Laws of Motion

Solution:

Free body diagram of $m$ is
image
$T = mg .....$(i)
Free body diagram of mass$\sqrt{2} $m is
image
$2T\: \cos \theta=\sqrt{2}mg ...(ii)$
Dividing Eq. (ii) by Eq. (i), we get
$\cos\theta=\frac{1}{\sqrt{2}}$ or $\theta =45^\circ$