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.

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

$A$ cart is moving with a velocity of $20 \, m/s$. Sand is being dropped into the cart at the rate of $50 \, kg/min$. The force required to move the cart with constant velocity will be ............ $N$.

$A$ rocket accelerates straight up by ejecting gas downwards. In a small time interval $\Delta t$,it ejects a gas of mass $\Delta m$ at a relative speed $u$. Calculate the kinetic energy $(KE)$ of the entire system at time $t + \Delta t$ and $t$,and show that the device that ejects gas does work equal to $(\frac{1}{2}) \Delta m u^2$ in this time interval (ignoring gravity).

$A$ metal block of $2 \,kg$ is at rest on a smooth plane. It is struck by a water jet releasing water at a rate of $1 \,kg \,s^{-1}$ with a speed of $5 \,ms^{-1}$. The acceleration of the block is: (in $\,ms^{-2}$)

$A$ 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 $N$)