$A$ 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 ............ $N$.

$A$ metal block of mass $4 \ kg$ is at rest on a frictionless surface. It is struck by a jet of water releasing $2 \ kg \ s^{-1}$ at a speed of $10 \ m \ s^{-1}$. The acceleration of the block is (in $m \ s^{-2}$)

$A$ rocket with a lift-off mass $20,000\; kg$ is blasted upwards with an initial acceleration of $5.0\; m s^{-2}$. Calculate the initial thrust (force) of the blast.

$A$ 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 $N$)

$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. The acceleration of the rocket $50 \ s$ after the blast,neglecting gravity,is $x \ ms^{-2}$. Find the value of $x$.

$A$ train is moving with a velocity of $20 \, m/s$. Dust is falling on it at the rate of $50 \, kg/min$. The extra force required to move this train with a constant velocity will be ....... $N$.