In a rocket of mass $1000\, kg$,fuel is consumed at a rate of $40\, kg/s$. The velocity of the gases ejected from the rocket is $5 \times 10^4\, m/s$. The thrust on the rocket is:

$A$ 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 $N$)

$A$ $5000\, kg$ 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 $.5$)

$A$ flexible chain of length $L = 2 \ m$ and mass $M = 1 \ kg$ is initially held in a vertical position such that its lower end just touches a horizontal surface. It is released from rest at time $t = 0$. Assuming that any part of the chain that strikes the plane immediately comes to rest and that the portion of the chain lying on the horizontal surface does not form any heap,find the height of its centre of mass above the surface at the instant $t = 1/\sqrt{5} \ s$ (before it completely comes to rest).

$A$ 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:

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 ....... $N$.