$A$ cart is moving with a velocity of $20 \, m/s$. Sand is being dropped into the cart at the rate of $50 \, kg/min$. The force required to move the cart with constant velocity will be ............ $N$.

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

Sand is being dropped from a stationary dropper at a rate of $0.5 \, kg s^{-1}$ on a conveyor belt moving with a velocity of $5 \, m s^{-1}$. The power needed to keep the belt moving with the same velocity will be: (in $, W$)

$A$ rocket works on the principle of conservation of which of the following?

Sand is being dropped on a conveyor belt at the rate of $2\,kg/s$. The force necessary to keep the belt moving with a constant speed of $3\,m/s$ will be ........... $N$.

$A$ 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: