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 $60°$and $30°$with the horizontal.

Then:
a. ${\mathrm{T}}_1=25$ $\mathrm{N}$                    
b. ${\mathrm{T}}_2=25$ $\mathrm{N}$
c. ${\mathrm{T}}_1=25\sqrt{3}$ $\mathrm{N}$               
d. ${\mathrm{T}}_2=25\sqrt{3}$ $\mathrm{N}$
Choose the correct option:

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

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. $\sqrt{2}Mg$

2. $\sqrt{2}mg$

3. $\sqrt{{(M+m)}^2+m^2}g$

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

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. \(18~\text{N}\)