$A$ rocket with a lift-off mass of $3.5 \times 10^4 \ kg$ is blasted upwards with an initial acceleration of $10 \ m/s^2$. The initial thrust of the blast is:

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

$A$ train is moving with a velocity of $20 \, m/s$. Dust is falling on it at the rate of $50 \, kg/min$. The extra force required to move this train with a constant velocity will be ....... $N$.

$A$ rocket with an initial mass $m_0$ is going up with a constant acceleration $a$ by exhausting gases with a velocity $v$ relative to the rocket motion. The mass of the rocket at any instant of time $t$ is (assume that no other forces act on it).

In a rocket of mass $1000\, kg$,fuel is consumed at a rate of $40\, kg/s$. The velocity of the gases ejected from the rocket is $5 \times 10^4\, m/s$. The thrust on the rocket is:

$A$ $5000\, kg$ rocket is set for vertical firing. The exhaust speed is $800\, m/s$. To give an initial upward acceleration of $20\, m/s^2$,the amount of gas ejected per second to supply the needed thrust will be ........... $kg/s$ $(g = 10\, m/s^2)$. (in $.5$)