A rocket has a mass of 100 kg. 90% of this is fuel. It ejects fuel vapours at the rate of 1 kg/sec with a velocity of 500 m/sec relative to the rocket. It is supposed that the rocket is outside the gravitational field. The initial upthrust on the rocket when it just starts moving upwards is:

1. Zero

2. 500 N

3. 1000 N

4. 2000 N

In which of the following cases, a force will not be required to keep the:

1. particle going in a circle.

2. particle going along a straight line.

3. momentum of the particle constant.

4. acceleration of the particle constant.

A ball of mass 150g starts moving with an acceleration of 20 m/s² when hit by a force, which acts on it for 0.1 sec. The impulsive force is:

1. 0.5 N-s

2. 0.1 N-s

3. 0.3 N-s

4. 1.2 N-s

A body, whose momentum is constant, must have a constant: 

1. force.

2. velocity.

3. acceleration.

4. All of these

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.

A force of 50 dynes is acted on a body of mass 5 g which is at rest for an interval of 3 seconds, then impulse is 

1. $0.15\times {10}^{-3}Ns$

2. $0.98\times {10}^{-3}Ns$

3. $1.5\times {10}^{-3}Ns$

4. $2.5\times {10}^{-3}Ns$

A bullet of mass 0.1 kg is fired with a speed of 100 m/sec, the mass of gun is 50 kg. The velocity of recoil is 

1. 0.2 m/sec

2. 0.1 m/sec

3. 0.5 m/sec

4. 0.05 m/sec

Three forces starts acting simultaneously on a particle moving with velocity $\overrightarrow{v}.$ These forces are represented in magnitude and direction by the three sides of a triangle ABC (as shown). The particle will now move with velocity 

1. $\overrightarrow{v}$ remaining unchanged

2. Less than $\overrightarrow{v}$

3. Greater than $\overrightarrow{v}$

4. $\overrightarrow{v}$ in the direction of the largest force BC

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force F applied on the upper string produces an acceleration of 2 m/s² in the upward direction in both the blocks. If T and T’ be the tensions in the two parts of the string, then 

1. T = 70.8 N and T’ = 47.2 N

2. T = 58.8 N and T’ = 47.2 N

3. T = 70.8 N and T’ = 58.8 N

4. T = 70.8 N and T’ = 40.2 N

A block is kept on a frictionless inclined surface with an angle of inclination 'α'. The incline is given an acceleration 'a' to keep the block stationary. Then a is equal to 

1. g

2. gtanα

3. g/tanα

4. gcosecα