Laws of Motion 2 Question 4

4. 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

(2001, 2M)

(a) $0^{\circ}$

(b) $30^{\circ}$

(c) $45^{\circ}$

(d) $60^{\circ}$

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Answer:

Correct Answer: 4. (c)

Solution:

  1. Free body diagram of $m$ is

Free body diagram of mass $\sqrt{2} m$ is

$$ 2 T \cos \theta=\sqrt{2} m g $$

Dividing Eq. (ii) by Eq. (i), we get

$$ \cos \theta=\frac{1}{\sqrt{2}} \text { or } \theta=45^{\circ} $$



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