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: 
 
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

A body of mass \(5\) kg is suspended by the strings making angles $\mathrm{}$\(60^\circ\) and $\mathrm{}$\(30^\circ\) with the horizontal.

 
Then:

In the shown system, each of the blocks is at rest. The value of \(\theta\) is:
 
1. \(\tan^{- 1} \left(1\right)\)
2. \(\tan^{- 1} \left(\frac{3}{4}\right)\)
3. \(\tan^{- 1} \left(\frac{4}{3}\right)\)
4. \(\tan^{- 1} \left(\frac{3}{5}\right)\)

Three blocks with masses of \(m\), \(2m\), and \(3m\) are connected by strings as shown in the figure. After an upward force \(F\) is applied on block \(m\), the masses move upward at a constant speed, \(v\). What is the net force on the block of mass \(2m\)? (\(g\) is the acceleration due to gravity). 

      

1.	\(2mg\)	2.	\(3mg\)
3.	\(6mg\)	4.	zero

A man of mass \(60\) kg is standing on the ground and holding a string passing over a system of ideal pulleys. A mass of \(10\) kg is hanging over a light pulley such that the system is in equilibrium. The force exerted by the ground on the man is: (\(g=\) acceleration due to gravity)

1. \(20g\)
2. \(45g\)
3. \(40g\)
4. \(60g\)

A string of negligible mass going over a clamped pulley of mass \(m\) supports a block of mass \(M\) as shown in the figure. The force on the pulley by the clamp is given by:
 
1. \(\sqrt{2} M g\)
2. \(\sqrt{2} m g\)
3. \(g\sqrt{\left( M + m \right)^{2} + m^{2}}\)
4. \(g\sqrt{\left(M + m \right)^{2} + M^{2}}\)

What is the minimum value of force \(F\) such that at least one block leaves the ground in the given figure? \(\left(g=10~\text{m/s}^2\right)\) $\mathrm{}$

A man of mass \(m\) stands on a crate of mass \(M\). He pulls on a light rope, passing over a smooth light pulley. The other end of the rope is attached to the crate. For the system to be in equilibrium, the force exerted by the man on the rope will be: