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 ....... $N$.

$A$ 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 $m \ s^{-2}$)

$A$ trolley containing water has a total mass of $4000\, kg$ and is moving at a speed of $40\, m/s$. Water starts leaking from a hole at the bottom of the trolley at a rate of $8\, kg/s$. What is the speed of the trolley after $50\, s$?

In a rocket,fuel burns at the rate of $2 \, kg/s$. This fuel is ejected from the rocket with a velocity of $80 \, km/s$. The force exerted on the rocket is ............. $N$.

$A$ Diwali cracker releases $25 \text{ g}$ of gas per second with a speed of $400 \text{ m/s}$ after an explosion. The force exerted by the gas on the cracker is:

An isolated rail car originally moving with speed $v_0$ on a straight,frictionless,level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions,and sand begins to pour out straight down relative to the rail car. What happens to the speed of the rail car as the sand pours out?