$A$ $2\,kg$ chain is in the form of a heap. Its length is $2\,m$. Its one end is being pulled at a constant speed of $2\,m/s$ horizontally. The power delivered to the chain is (in $W$).

$A$ rocket lifts off from the ground and accelerates upwards at $1 \ m \ s^{-2}$. $20 \ s$ after liftoff, a piece breaks off from the bottom of the rocket. After breaking off, how much time does it take approximately to reach the ground (in $s$)? (Take $g = 10 \ m \ s^{-2}$)

In a rocket,fuel burns at the rate of $1\; kg/s$. This fuel is ejected from the rocket with a velocity of $60\; km/s$. This exerts a force on the rocket equal to ......... $N$.

$A$ sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root of speed $v$ of the belt,i.e.,$\frac{dm}{dt} \propto \sqrt{v}$. If $P$ is the power delivered to run the belt at constant speed,then which of the following relationships is true?

$A$ balloon has a mass of $10\,g$ in air. The air escapes from the balloon at a uniform rate with a velocity of $4.5\,cm/s$. If the balloon shrinks completely in $5\,s$,then the average force acting on the balloon will be (in $dyne$).

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