$A$ 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:

$A$ metal block of $2 \,kg$ is at rest on a smooth plane. It is struck by a water jet releasing water at a rate of $1 \,kg \,s^{-1}$ with a speed of $5 \,ms^{-1}$. The acceleration of the block is: (in $\,ms^{-2}$)

At a certain instant of time,the mass of a rocket going up vertically is $100 \, kg$. If it is ejecting $5 \, kg$ of gas per second at a speed of $400 \, m/s$,the acceleration of the rocket would be ........ $m/s^2$ (taking $g = 10 \, m/s^2$).

$A$ rocket has a mass of $100 \, kg$. $90\%$ of this is fuel. It ejects fuel vapours at the rate of $1 \, kg/s$ with a velocity of $500 \, m/s$ relative to the rocket. It is assumed that the rocket is outside the gravitational field. The initial upthrust on the rocket when it just starts moving upwards is ......... $N$.

Rocket engines lift a rocket from the earth's surface because hot gas with high velocity

$A$ 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.