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 string of length L is fixed at one end and carries a mass M at the other end. The string makes 2/π revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is 

(1) ML

(2) 2 ML

(3) 4 ML

(4) 16 ML

A long horizontal rod has a bead which can slide along its length, and 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 $\alpha$. 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) $\sqrt{\frac{\mu }{\alpha }}$

(2) $\frac{\mu }{\sqrt{\alpha }}$

(3) $\frac{1}{\sqrt{\mu \alpha }}$

(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 the momentum.

(3) change the direction.

(4) keep it moving with uniform velocity.

A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end (see 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  Question, 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 t₁ to reach the floor when lift is stationary. It takes time t₂ when the lift is moving up with constant acceleration. Then:

(1) t₁ > t₂

(2) t₂ > t₁

(3) t₁ = t₂

(4) t₁ >> t₂

If the tension in the cable of 1000 kg elevator is 1000 kg weight, the elevator:

(1) is accelerating upwards.

(2) is accelerating downwards.

(3) may be at rest or accelerating.

(4) may be at rest or in uniform motion.