$A$ 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.

$A$ block of metal weighing $2 \,kg$ is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of $1 \,kg \,s^{-1}$ and at a speed of $10 \,m \,s^{-1}$. Then,the initial acceleration of the block,in $m \,s^{-2}$,will be:

$A$ rocket with a lift-off mass $2 \times 10^4\,kg$ is blasted upwards with an initial acceleration of $5\,m\,s^{-2}$. The initial thrust of the blast is (Take $g = 10\,m\,s^{-2}$).

$A$ railway wagon of mass $5 \times 10^3 \ kg$ is moving with an initial velocity of $1.2 \ m/s$ on frictionless rails. Rain falls vertically into the wagon. When $10^3 \ kg$ of water has collected in the wagon,what is the change in the kinetic energy of the wagon in $J$?

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 ....... $N$.

$A$ Diwali rocket of mass $100\,g$ lifts up with an acceleration of $5\,m/s^2$. If gases eject out of the rocket at a rate of $10\,g/s$,then find the velocity of ejection of gas with respect to the rocket in $m/s$.