Sand is being dropped on a conveyor belt at the rate of $2\,kg/s$. The force necessary to keep the belt moving with a constant speed of $3\,m/s$ will be ........... $N$.

$A$ flat plate moves normally with a speed $v_1$ towards a horizontal jet of water of uniform area of cross-section. The jet discharges water at the rate of volume $V$ per second at a speed of $v_2$. The density of water is $\rho$. Assume that water splashes along the surface of the plate at right angles to the original motion. The magnitude of the force acting on the plate due to the jet of water is

$A$ rocket works on the principle of conservation of which of the following?

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 can go vertically upwards in the Earth's atmosphere because

$A$ trolley containing water has a total mass of $4000\, kg$ and is moving at a speed of $40\, m/s$. Water starts leaking from a hole at the bottom of the trolley at a rate of $8\, kg/s$. What is the speed of the trolley after $50\, s$?