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:

$A$ $5000\, kg$ rocket is set for vertical firing. The exhaust speed is $800\, m/s$. To give an initial upward acceleration of $20\, m/s^2$,the amount of gas ejected per second to supply the needed thrust will be ........... $kg/s$ $(g = 10\, m/s^2)$. (in $.5$)

At a certain instant of time,the mass of a rocket going up vertically is $100 \, kg$. If it is ejecting $5 \, kg$ of gas per second at a speed of $400 \, m/s$,the acceleration of the rocket would be ........ $m/s^2$ (taking $g = 10 \, m/s^2$).

In a rocket,fuel burns at the rate of $1\; kg/s$. This fuel is ejected from the rocket with a velocity of $60\; km/s$. This exerts a force on the rocket equal to ......... $N$.

$A$ satellite moving with velocity $v$ in a force-free space collects stationary interplanetary dust at a rate of $\frac{dM}{dt} = \alpha v$,where $M$ is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is:

$A$ rifle of $20 \,kg$ mass can fire $4$ bullets per second. The mass of each bullet is $35 \times 10^{-3} \,kg$ and its final velocity is $400 \,ms^{-1}$. What force must be applied on the rifle so that it does not move backwards while firing the bullets (in $\,N$)?