$A$ rocket is ejecting $50\,g$ of gases per second at a speed of $500\,m/s.$ The accelerating force on the rocket will be ............ $N$.

$A$ $2\,kg$ 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 $W$).

$A$ 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 $m/s$.

$A$ 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 $g = 10\,m\,s^{-2}$).

$A$ cart is moving with a velocity of $20 \, m/s$. Sand is being dropped into the cart at the rate of $50 \, kg/min$. The force required to move the cart with constant velocity will be ............ $N$.

$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. The acceleration of the rocket $50 \ s$ after the blast,neglecting gravity,is $x \ ms^{-2}$. Find the value of $x$.