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 small coin is kept at a distance r from the centre of a gramophone disc rotating at an angular speed $\omega$. The minimum coefficient of friction for which a coin will not slip is:

1.  $\frac{{\mathrm{r\omega }}^2}{\mathrm{g}}$

2.  $\frac{\mathrm{g}}{{\mathrm{r\omega }}^2}$

3.  $\frac{{\mathrm{r}}^2{\mathrm{\omega }}^2}{\mathrm{g}}$

4.  $\frac{\mathrm{r\omega }}{\mathrm{g}}$

A plank with a box on it at one end is gradually raised at the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank, respectively, will be:
    

A block \(A\) of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body \(B\) of mass 3 kg at the other end. The acceleration of the system will be: (given \(g\) = 10 ms^–2)

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

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

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