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 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

A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively 

1. g, g

2. g – a, g – a

3. g – a , g

4. a, g

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be 

1. $mg \cos \theta$

2. $mg \sin \theta$

3. mg

4. $mg/\cos \theta$

A particle moves in the \(XY\text-\)plane under the action of a force \(F\) such that the components of its linear momentum \(p\) at any time \(t\) are \(p_x = 2 \cos t\),  \(p_y = 2 \sin t\). The angle between \(F\) and \(p\) at time \(t\) will be:

On a stationary sailboat, the air is blown at the sails from a fan attached to the boat. The boat will:

1. remain stationary

2. spin around

3. move in a direction opposite to that in which air is blown

4. move in the direction in which the air is blown

The tension in the spring is 

1. Zero

2. 2.5 N

3. 5 N

4. 10 N

Rocket engines lift a rocket from the earth surface because hot gases with high velocity:

1. push against the earth.

2. push against the air.

3. react against the rocket and push it up.

4. heat up the air which lifts the rocket.

The mass of a body measured by a physical balance in a lift at rest is found to be m. If the lift is going up with an acceleration a, its mass will be measured as:

1. $m\left(1-\frac{{\displaystyle a}}{{\displaystyle g}}\right)$

2. $m\left(1+\frac{{\displaystyle a}}{{\displaystyle g}}\right)$

3. m

4. Zero

Three weights W, 2W and 3W are connected to identical springs suspended from a rigid horizontal rod. The assembly of the rod and the weights fall freely. The positions of the weights from the rod are such that 

1. 3W will be farthest

2. W will be farthest

3. All will be at the same distance

4. 2W will be farthest