$A$ 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:

Sand is being poured at a rate of $50 \, kg/min$ into a train moving with a velocity of $20 \, m/s$. To maintain the constant velocity of the train,the force required is ........ $N$.

$A$ rocket is fired vertically from the ground with a resultant vertical acceleration of $10 \,m/s^2$. The fuel is exhausted in $1 \,min$ and it continues to move up. What is the maximum height reached (in $\,km$)?

$A$ balloon with mass $m$ is descending vertically with an acceleration $a$ (where $a < g$). The mass to be removed from the balloon so that it starts moving vertically up with an acceleration $a$ is:

$A$ machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant,the gun fires bullets of mass $10 \,g$ with a velocity of $500 \,m/s$ with respect to the car. If the number of bullets fired per second is $10$,the acceleration of the car will be ..... $m/s^2$.

Sand is deposited at a uniform rate of $20 \ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10 \ m/min$. Find the force required to maintain the constant velocity of the conveyor belt.