$A$ $6000 \,kg$ rocket is set for firing. If the exhaust speed is $1000 \,m/s$,how much gas must be ejected each second to supply the thrust needed to overcome the weight of the rocket?

$A$ satellite moving with velocity $v$ in a force-free space collects stationary interplanetary dust at a rate of $\frac{dM}{dt} = \alpha v$,where $M$ is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is:

$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. What is the acceleration of the rocket $50 \ s$ after the launch,neglecting gravity (in $m/s^2$)?

$A$ rocket of mass $1000 \, kg$ exhausts gases at a rate of $4 \, kg/s$ with a velocity of $3000 \, m/s$. The thrust developed on the rocket is ........ $N$.

In a rocket, fuel burns at the rate of $1 \,kg / s$. This fuel is ejected from the rocket with a velocity of $60 \,km / s$. The force exerted on the rocket by this is (in $\,N$)

$A$ balloon has $2 \,g$ of air. $A$ small hole is pierced into it. The air comes out with a velocity of $4 \,m/s$. If the balloon shrinks completely in $2.5 \,s$,the average force acting on the balloon is ..........$N$.