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

Is the formula $\vec{F} = m\vec{a}$ valid in all circumstances? Why?

$A$ 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:

$A$ 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.

$A$ machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant,the gun fires bullets of mass $10 \,g$ with a velocity of $500 \,m/s$ with respect to the car. The number of bullets fired per second is $10$. The average thrust on the system is ........ $N$.

Bullets of mass $50 \, g$ are fired from a gun of mass $10 \, kg$ with a velocity of $300 \, m/s$. If $5$ bullets are fired per second,then what force must a person apply on the gun so that it does not recoil? $(N)$