$A$ 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 $50\, s$?

$A$ block of metal weighing $2 \,kg$ is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of $1 \,kg \,s^{-1}$ and at a speed of $10 \,m \,s^{-1}$. Then,the initial acceleration of the block,in $m \,s^{-2}$,will be:

Sand is being dropped on a conveyor belt at the rate of $M \ kg/s$. The force necessary to keep the belt moving with a constant velocity of $v \ m/s$ will be

$A$ 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 ....... $N$.

If the force on a rocket having an exhaust velocity of $300 \, m/s$ is $210 \, N$,then the rate of combustion of the fuel is ........... $kg/s$.