$A$ 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.

$A$ rocket is fired vertically up from the ground with a resultant acceleration of $10\,m/s^2$. The fuel is finished in $1\,min$ and it continues to move up. 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 ......... $N$.

$A$ rocket which has a 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 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).

$A$ 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?