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) $2.5\times {10}^{-3}Ns$

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

A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block will be: 

(1) P

(2) $\frac{Pm}{M+m}$

(3) $\frac{PM}{M+m}$

(4) $\frac{Pm}{M-m}$