$A$ metal block of $2 \,kg$ is at rest on a smooth plane. It is struck by a water jet releasing water at a rate of $1 \,kg \,s^{-1}$ with a speed of $5 \,ms^{-1}$. The acceleration of the block is: (in $\,ms^{-2}$)

In a rocket of mass $1000\, kg$,fuel is consumed at a rate of $40\, kg/s$. The velocity of the gases ejected from the rocket is $5 \times 10^4\, m/s$. The thrust on the rocket is:

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 ........... $kg/s$.

$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt} = \alpha v$,where $M$ is the mass,$v$ is the velocity of the satellite,and $\alpha$ is a constant. What is the deceleration of the satellite?

$A$ heap of rope with mass density $\lambda$ (per unit length) lies on a table. You grab one end and pull horizontally with constant speed $v$,as shown in the figure. (Assume that the rope has no friction with itself in the heap.) The force that you must apply to maintain the constant speed $v$ is

$A$ 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).