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

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, the spring balance is massless, so the reading of the 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 the 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 \(500\) grams 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