The figure shows a rod of length 5 m. Its ends, A and B, are restrained to moving in horizontal and vertical guides. When the end A is 3 m above O, it moves at 4 m/s. The velocity of end B at that instant is:
         

1. 2 m/s

2. 3 m/s

3. 4 m/s

4. 0.20 m/s

If the block is being pulled by the rope moving at speed v as shown, then the horizontal velocity of the block is:

1.  v

2.  vcos$\mathrm{\theta }$

3.  $\frac{\mathrm{v}}{\cos \mathrm{\theta }}$

4.  $\frac{\mathrm{v}}{\sin \mathrm{\theta }}$

In the given figure, spring balance is massless, so the reading of spring balance will be:
                     

The strings and pulleys shown in the figure are massless. The reading shown by the light spring balance S is:

What is the velocity of the block when the angle between the string and horizontal is \(30^\circ\) as shown in the diagram?

          
1. \(v_B=v_P\)
2. \(v_B=\frac{v_P}{\sqrt{3}}\)
3. \(v_B=2v_P\)
4. \(v_B=\frac{2v_P}{\sqrt{3}}\)

A bucket full of water tied with the help of a 2 m long string performs a vertical circular motion. The minimum angular velocity of the bucket at the uppermost point so that water will not fall will be:

1. 2$\sqrt{5}$ rad/s

2. $\sqrt{5}$ rad/s

3. 5 rad/s

4. 10 rad/s

A mass of 4 kg is suspended as shown in the figure with the help of massless inextensible string A. Another identical string, B, is connected at the lower end of the block. When a sudden pulling downward jerk slightly greater than the breaking strength of A and B is given to string B, then:
    
1. String A will break
2. String B will break
3. Both A and B will break simultaneously
4. Both A and B will never break

A 0.5 kg body experiences a force \(F=(2+3x^2)\) N, where \(x\) in metres is the displacement from the origin. If it is released to move along the X-axis from the origin, then its initial acceleration is:

On the application of an impulsive force, a sphere of mass \(500\) g starts moving with an acceleration of \(10\) m/s². The force acts on it for \(0.5\) s. The gain in the momentum of the sphere will be:

1. \(2.5\) kg-m/s

2. \(5\) kg-m/s

3. \(0.05\) kg-m/s

4. \(25\) kg-m/s

Three identical masses, each of mass 4 kg, are connected by massless inextensible strings. The string joining A and B passes over a massless frictionless pulley as shown in the figure. The tension in the string connecting mass B and C is:

1. 40 N

2. 20 N

3. 26.67 N

4. 13.33 N