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)

Two masses, M and m, are attached to a vertical axis by weightless threads of combined length l. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity ω. If the tensions in the threads are the same during motion, the distance of M from the axis is:

1. $\frac{Ml}{M+m}$

2. $\frac{ml}{M+m}$

3. $\frac{M+m}{M}l$

4. $\frac{M+m}{m}l$

A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. The normal force on the motorcycle as it ascends the overbridge will be:

1.  increases.

2.  decreases.

3.  remains the same.

4.  fluctuates erratically.

A block is placed on a rough horizontal plane. A time dependent horizontal force, \(F=kt,\) acts on the block. The acceleration time graph of the block is :

1.		2.
3.		4.

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: