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:

A metal sphere is suspended from a wall by a string. The forces acting on the sphere are shown in the figure. Which of the following statements is NOT correct?
   $\mathrm{}$

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. \(\sqrt{\left( M + m \right)^{2} + m^{2}} g\)
4. \(\sqrt{\left(M + m \right)^{2} + M^{2}} g\)

Three blocks \(\mathrm{A}\), \(\mathrm{B}\), and \(\mathrm{C}\) of masses \(4~\text{kg}\), \(2~\text{kg}\), and \(1~\text{kg}\) respectively, are in contact on a frictionless surface, as shown. If a force of \(14~\text{N}\) is applied to the \(4~\text{kg}\) block, then the contact force between \(\mathrm{A}\) and \(\mathrm{B}\) is: 
          
1. \(2~\text{N}\)
2. \(6~\text{N}\)
3. \(8~\text{N}\)
4. \(18~\text{N}\)