$A$ rocket works on the principle of conservation of which of the following?

$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t} = \alpha v$,where $M$ is the mass,$v$ is the speed of the satellite,and $\alpha$ is a constant. The acceleration of the satellite is:

An open carriage in a goods train is moving with a uniform velocity of $10 \,m/s$. If the rain adds water with zero velocity at the rate of $5 \,kg/s$,then the additional force required by the engine to maintain the same velocity of the train is ....... $N$.

The rate of fuel consumption in a rocket is $40 \ kg/s$. The velocity of the exhaust gases coming out of the rocket is $5 \times 10^4 \ m/s$. What is the thrust force acting on the rocket?

In a rocket of mass $1000\, kg$,fuel is consumed at a rate of $40\, kg/s$. The velocity of the gases ejected from the rocket is $5 \times 10^4\, m/s$. The thrust on the rocket is:

$A$ gun of mass $10 \, kg$ fires $4$ bullets per second. The mass of each bullet is $20 \, g$ and the velocity of the bullet when it leaves the gun is $300 \, m/s$. The force required to hold the gun while firing is (in $N$)