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.

An object with a mass 10 kg moves at a constant velocity of 10 m/sec. A constant force then acts for 4 second on the object and gives it a speed of 2 m/sec in opposite direction. The acceleration produced in it, is 

(1) 3 m/sec²

(2) –3 m/sec²

(3) 0.3 m/sec²

(4) –0.3 m/sec²

A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant the gun fires bullets of mass 10 gm with a velocity of 500 m/sec with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is 

(1) 550 N

(2) 50 N

(3) 250 N

(4) 250 dyne

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

1. 0.25 m/sec²

2. 2.5 m/sec²

3. 5.0 m/sec²

4. 0.025 m/sec²