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

If the force on a rocket having an exhaust velocity of $300 \, m/s$ is $210 \, N$,then the rate of combustion of the fuel is ........... $kg/s$.

$A$ solid disc of mass $M$ is held horizontally in the air by throwing $40$ stones per second vertically upwards to strike the disc,each with a velocity of $6\,m/s$. If the mass of each stone is $0.05\,kg$,what is the mass of the disc in $kg$? (Take $g = 10\,m/s^2$)

Consider a rocket is being fired. The kinetic energy of the rocket is increased by $16$ times, whereas its total mass is reduced by half through the burning of fuel. The factor by which its momentum increases is

$A$ balloon with mass $m$ is descending vertically with an acceleration $a$ (where $a < g$). The mass to be removed from the balloon so that it starts moving vertically up with an acceleration $a$ is:

$A$ block of metal weighing $2 \,kg$ is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of $1 \,kg \,s^{-1}$ and at a speed of $10 \,m \,s^{-1}$. Then,the initial acceleration of the block,in $m \,s^{-2}$,will be: