A body of mass \(0.4\ \text{kg}\) is whirled in a vertical circle, making \(2\ \text{rev/s}\). If the radius of the circle is \(2\ \text{m}\), then the tension in the string when the body is at the top of the circle is:

1. \(41.56\ \text{N}\)
2. \(89.86\ \text{N}\)
3. \(109.86\ \text{N}\)
4. \(122.4\ \text{N}\)

A bucket full of water is revolved in vertical circle of radius 2m. What should be the maximum time-period of revolution so that the water doesn't fall off the bucket ?

1. 1 sec

2. 2 sec

3. 3 sec

4. 4 sec

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is 

1. $\frac{ML{\omega }^2}{2}$

2. $ML{\omega }^2$

3. $\frac{ML{\omega }^2}{4}$

4. $\frac{M{L}^2{\omega }^2}{2}$

A car is moving in a circular horizontal track of radius \(10~\text{m}\) with a constant speed of \(10~\text{m/s}\). A plumb bob is suspended from the roof of the car by a light rigid rod of length \(1.00~\text{m}\). The angle formed by the rod with respect to the vertical is:

A long horizontal rod has a bead that can slide along its length and is initially placed at a distance \(L\) from one end \(A\) of the rod. The rod is set in angular motion about \(A\) with constant angular acceleration \(𝛼\). If the coefficient of friction between the rod and the bead is \(μ\), and gravity is neglected, then the time after which the bead starts slipping is:

1. \(\sqrt{\dfrac{\mu}{\alpha}}\)
2. \(\dfrac{\mu}{\sqrt{\alpha}}\)
3. \(\dfrac{1}{\sqrt{\mu\alpha}}\)
4. Infinitesimal

A particle is moving with a constant speed along a straight-line path. A force is not required to:

1. increase its speed.
2. decrease its momentum.
3. change its direction.
4. keep it moving with uniform velocity.

A mass of \(1\ \text{kg}\) is suspended by a string \(A\). Another string \(C\) is connected to its lower end as shown in the given figure. If a sudden jerk is given to \(C\), then:

1. The portion \(AB\) of the string will break
2. The portion \(BC\) of the string will break
3. None of the strings will break
4. The mass will start rotating

In the given figure, a mass \(m\) is suspended by string \(A\). Another string \(C\) is connected to its lower end. If the string \(C\) is stretched slowly, then:

1. The portion \(AB\) of the string will break
2. The portion \(BC\) of the string will break
3. None of the strings will break
4. None of the above

Newton's second law gives the measure of:

1. Acceleration
2. Force
3. Momentum
4. Angular momentum

A coin is dropped in a lift. It takes time \(t_1\) to reach the floor when the lift is stationary. It takes time \(t_2\) when the lift is moving up with constant acceleration. Then:
1. \(t_1 > t_2\)
2. \(t_1 < t_2\)
3. \(t_1 = t_2\)
4. \(t_1 >> t_2\)