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 ......... $N$.

$A$ soldier with a machine gun,falling from an airplane,gets detached from his parachute. He is able to resist the downward acceleration if he shoots $40$ bullets per second at a speed of $500 \,m/s$. If the mass of a bullet is $49 \,g$,what is the mass of the man with the gun in $kg$? Ignore air resistance and assume the acceleration due to gravity $g = 9.8 \,m/s^2$.

Sand is being poured at a rate of $50 \, kg/min$ into a train moving with a velocity of $20 \, m/s$. To maintain the constant velocity of the train,the force required is ........ $N$.

$A$ 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:

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 ....... $N$.

$A$ rocket is ejecting $50\,g$ of gases per second at a speed of $500\,m/s.$ The accelerating force on the rocket will be ............ $N$.