A ball of mass \(0.25\ \text{kg}\) attached to the end of a string of length \(1.96\ \text{m}\) is moving in a horizontal circle. The string will break if the tension is more than \(25\ \text{N}\). What is the maximum speed with which the ball can be moved:

1. \(14\ \text{m/s}\)

2. \(3\ \text{m/s}\)

3. \(3.92\ \text{m/s}\)

4. \(5\ \text{m/s}\)

A body of mass \(5\ \text{kg}\) is moving in a circle of radius \(1\ \text{m}\) with an angular velocity of \(2\ \text{rad/s}\). The centripetal force is:

1. \(10\ \text{N}\)

2. \(20\ \text{N}\)

3. \(30\ \text{N}\)

4. \(40\ \text{N}\)

A stone of mass \(16\ \text{kg}\) is attached to a string \(144\ \text{m}\) long and is whirled in a horizontal circle. The maximum tension the string can withstand is \(16\) Newton. The maximum velocity of revolution that can be given to the stone without breaking it will be:

1. \(20\ \text{ms}^{–1}\)
2. \(16\ \text{ms}^{–1}\)
3. \(14\ \text{ms}^{–1}\)
4. \(12\ \text{ms}^{–1}\)

The coefficient of friction between the road and tyre is \(0.2\). The maximum velocity for skidding of a car moving on a circular track of radius \(100\ \text{m}\) is:

1. \(0.14\ \text{m/s}\)

2. \(140\ \text{m/s}\)

3. \(1.4\ \text{m/s}\)

4. \(14\ \text{m/s}\)

A ball of mass \(0.1~\text{kg}\) is whirled in a horizontal circle of radius \(1\) m by means of a string at an initial speed of \(10~\text{rpm}\) . Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is:

A cyclist riding a bicycle at a speed of \(14\sqrt3\ \text{ms}^{–1}\) takes a turn around a circular road of radius \( 20\sqrt3\ \text{m}\) without skidding. His inclination to the vertical is:

1. \(30^\circ\)

2. \(​​90^\circ\)

3. \(45^\circ\)

4. \(60^\circ\)

A point mass \(m\) is suspended from a light thread of length \(l,\) fixed at \(O\), and is whirled in a horizontal circle at a constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are:

1.		2.
3.		4.

If a cyclist moving at a speed of \(4.9\ \text{m/s}\) on a level road can take a sharp circular turn of radius \(4\ \text{m}\), then the coefficient of friction between the cycle tyres and the road is:

1. \( 0.41\)
2. \(0.51\)
3.\( 0.61\)
4. \(0.71\)

A motorcycle driver doubles his velocity when he is taking a turn. The force exerted outwardly will be:

1. Double
2. Half
3. \(4\) times
4. \( \frac 14\)

Two bodies of equal mass revolve in circular orbits of radii \(R_1\) and \(R_2\) with the same period. Their centripetal forces are in the ratio:
1. \(\left(\dfrac{R_2}{R_1}\right)^2\)
2. \(\dfrac{R_1}{R_2}\)
3. \(\left(\dfrac{R_1}{R_2}\right)^2\)
4. \(\sqrt{R_1R_2}\)