In a certain gravity free space, the piston of an injection is being pushed so that the water jet comes out with a speed v. The area of the piston is much greater than the orifice of the injection.

Options

A. The force required to be applied on the piston is proportional to `v^(2)`.
B. The power developed by the force pushing the piston is proportional to `v^3`.
C. The time for emptying the injection is proportional to `v^(-1)`.
D. The total work done in emptying the injection is proportional to `v^2`.

Explanation

`F/A+1/2 rhov'^(2) =1/2 rhov^(2)` (i)
`A'v'=Av (ii)`
`:. Fpropv^(2) (A)`
`P=F.v' (B)`
`Av`=volume flow rate =volume/t
`:. t prop 1/v (C)`
`W.D.=DeltaKrArr (D)`