A vessel completely filled wit water is suspended with help of strings from a spring balance as shwon in figure. A cork is plugged at the bottom of the vessel. If the initial reading of the spring balannce is `W_(0)`. Then the reading of the spring balance just after the cork is removed and the liquid begins to flow out will be `[rho=` density of liquid & A=coss -sectional area of narrow pipe]

Options

A. `W_(0)+rhogHA`
B. `W_(0)+2rhogHA`
C. `W_(0)-rhogHA`
D. `W_(0)-2rhogHA`

Answer

D

Explanation

Momentum of water following out of the tube in time `Delta=Deltap=rhoAv^(2)Deltat` where `v=sqrt(2gH)`
`thereforeFDeltat=Deltap=rhoAv^(2)Deltat`
or `F=rhoAv^(2)=2rhogHA`
`therefore` Reading of spring balance `=W_(0)-2rhogHA`