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

Sand is being dropped on a conveyor belt at the rate of $2\,kg/s$. The force necessary to keep the belt moving with a constant speed of $3\,m/s$ will be ........... $N$.

Sand is deposited at a uniform rate of $20 \ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10 \ m/min$. Find the force required to maintain the constant velocity of the conveyor belt.

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

$A$ rocket of mass $4000\, kg$ is set for vertical firing. How much gas must be ejected per second so that the rocket may have an initial upward acceleration of magnitude $19.6\, m/s^2$? [Exhaust speed of fuel $= 980\, m/s$.]

$A$ 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 $\,N$)?