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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 be:Physics Question Image

WBJEEWBJEE 2006

Solution:

From force diagram shown in figure, $ T=mg $ ...(i) and $ 2T\cos \theta =\sqrt{2}mg $ ...(ii) Combining Eqs.(i) and (ii), we have
$ 2m\,\cos \theta =\sqrt{2}\,mg $ or $ \cos \theta =\frac{1}{\sqrt{2}} $ or $ \theta ={{45}^{o}} $

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