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 $, W$)

Gravels are dropped on a conveyor belt at the rate of $0.5 \, kg/s$. The extra force required in newtons to keep the belt moving at $2 \, m/s$ is

$A$ $2\,kg$ chain is in the form of a heap. Its length is $2\,m$. Its one end is being pulled at a constant speed of $2\,m/s$ horizontally. The power delivered to the chain is (in $W$).

$A$ balloon has a mass of $10\,g$ in air. The air escapes from the balloon at a uniform rate with a velocity of $4.5\,cm/s$. If the balloon shrinks completely in $5\,s$,then the average force acting on the balloon will be (in $dyne$).

An ice block is melting at a constant rate $\left| \frac{dm}{dt} \right| = \mu$. Its initial mass is $m_0$ and it is moving with velocity $v$ on a frictionless horizontal surface. The distance travelled by it until it melts completely is:

$A$ rocket motor consumes $100 \ kg$ of fuel per second,exhausting it with a speed of $5 \ km/s$. The speed of the rocket when its mass is reduced to $\frac{1}{20}$ of its initial mass is (Assume initial speed to be zero and ignore gravitational and viscous forces.)