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. \(t_1 >> t_2\)

If the tension in the cable of \(1000~\text{kg}\) elevator is \(1000~\text{kg}\) 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.

An object with a mass \(10\ \text{kg}\) moves at a constant velocity of \(10\ \text{m/s}\). A constant force then acts for \(4\) seconds on the object and gives it a speed of \(2\ \text{m/s}\) in the opposite direction. The acceleration produced in it is:
1. \(3\ \text{m/s}^2\)
2. \(-3\ \text{m/s}^2\)
3. \(0.3\ \text{m/s}^2\)
4. \(-0.3\ \text{m/s}^2\)

A machine gun is mounted on a \(2000\ \text{kg}\) car on a horizontal frictionless surface. At some instant, the gun fires bullets of mass \(10\ \text{g}\) with a velocity of \(500\ \text{m/s}\) with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is:

1. \(550\ \text{N}\)
2. \(50\ \text{N}\)
3. \(250\ \text{N}\)
4. \(250\ \text{dyn}\)

In the given diagram, the acceleration of the car will be:

1. \(0.25\ \text{m/s}^2\)
2. \(2.5\ \text{m/s}^2\)
3. \(5.0\ \text{m/s}^2\)
4. \(0.025\ \text{m/s}^2\)