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

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. \(\dfrac{rω^{2}}{g}\)
2. \(\dfrac{g}{r\omega^2}\)
3. \(\dfrac{r^2ω^{2}}{g}\)
4. \(\dfrac{rω}{g}\)

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 \(30^{\circ}\), 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 \(g=10~\text{m/s}^2)\)

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 \(\omega\). If the tensions in the threads are the same during motion, the distance of \(M\) from the axis is:
1. \(\frac{M l}{M + m}\)
2. \(\frac{m l}{M + m}\)
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. \(v\cos\theta\)
3. \(\frac{v}{\cos\theta}\)
4. \(\frac{v}{\sin\theta}\)

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