$A$ $600\; kg$ rocket is set for a vertical firing. If the exhaust speed is $1000\; m/s$,the mass of the gas ejected per second (in $kg/s$) to supply the thrust needed to overcome the weight of the rocket is

Consider a rocket is being fired. The kinetic energy of the rocket is increased by $16$ times, whereas its total mass is reduced by half through the burning of fuel. The factor by which its momentum increases is

$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \,m/s^2$. If after $5 \,s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be.........$m$

$A$ stationary rocket of initial mass $m_0$ is expelling exhaust gas at a steady speed $v_e$ with respect to itself. There is no external force on the rocket. When its mass is reduced to $\frac{m_0}{2}$,the velocity attained by the rocket will be:

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 ....... $N$.

$A$ flexible chain of length $L = 2 \ m$ and mass $M = 1 \ kg$ is initially held in a vertical position such that its lower end just touches a horizontal surface. It is released from rest at time $t = 0$. Assuming that any part of the chain that strikes the plane immediately comes to rest and that the portion of the chain lying on the horizontal surface does not form any heap,find the height of its centre of mass above the surface at the instant $t = 1/\sqrt{5} \ s$ (before it completely comes to rest).