For a rocket moving in free space, the fraction of mass to be disposed of Off to attain a speed equal to two times the exhaust speed is given by (given ${\mathrm{e}}^2$ = 7.4)

1. 0.40

2.  0.37

3.  0.50

4.  0.86

If force on a rocket having exhaust velocity of 300 m/sec is 210 N, then rate of combustion of the fuel is 

(1) 0.7 kg/s

(2) 1.4 kg/s

(3) 0.07 kg/s

(4) 10.7 kg/s

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms^–1. To give an initial upward acceleration of 20 ms^–2, the amount of gas ejected per second to supply the needed thrust will be (g = 10 ms^–2) 

(1) 127.5 kg s^–1

(2) 187.5 kg s^–1

(3) 185.5 kg s^–1

(4) 137.5 kg s^–1

A satellite in force-free space sweeps stationary interplanetary dust at a rate $dM/dt=\alpha v$ where M is the mass, v is the velocity of the satellite and $\alpha$ is a negative constant. What is the deacceleration of the satellite?

(1) $-2\alpha v^2/M$

(2) $-\alpha v^2/M$

(3) $+\alpha v^2/M$

(4) $-\alpha v^2$

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

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.

Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be 

1. Mv newton 

2. 2Mv newton 

3. $\frac{Mv}{2}$newton 

4. zero