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

Two masses, A and B, of mass 4 kg and 1 kg, respectively, are connected with the help of a massless inextensible string. Mass A is placed on a rough horizontal table, and mass B is suspended with the help of a string passing through a smooth hole at the centre of the table. For the system to be in equilibrium, what should be the minimum value of the coefficient of friction?

1. 0.5

2. 0.25

3. 2.5

4. 0.125