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

$A$ sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root of speed $v$ of the belt,i.e.,$\frac{dm}{dt} \propto \sqrt{v}$. If $P$ is the power delivered to run the belt at constant speed,then which of the following relationships is true?

$A$ $5000\, kg$ rocket is set for vertical firing. The exhaust speed is $800\, m/s$. To give an initial upward acceleration of $20\, m/s^2$,the amount of gas ejected per second to supply the needed thrust will be ........... $kg/s$ $(g = 10\, m/s^2)$. (in $.5$)

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

$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $20\, m/s^2$. If after $5\, s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be......$m$

$A$ cart loaded with sand is moving with velocity $v$. Sand is falling through a hole as shown in the diagram. After falling on the ground,the sand is: