The range of water flowing out of a small hole made at a depth `10 m` below water surface in a large tank is `R`. Find the extra pressure (in atm) applied on the water surface so that range becomes `2R`. Take `1atm=10^(5)Pa`.

Options

A. 9 atm
B. 4 atm
C. 5 atm
D. 3 atm

Answer

D

Explanation

To make range R' = 2R
`v' xx t =2vxxt " "impliesv'=2v`
Applying Bernoulli's theorem in first case.
`P+(1)/(2)rho(0)^(2)+rhogh=P+(1)/(2)rhov^(2)+0" "implies " "rhogh=(1)/(2)rhov^(2)" "....(1)`
in second case
`(P+DeltaP)+(1)/(2)rho(0)^(2)+rhogh=P+(1)/(2)rhov'^(2)+0implies" "DeltaP=(1)/(2)rho(2v)^(2)-rhogh" "....(2)`
From (1) `&` (2)
`DeltaP=3rhogh" "impliesDeltaP=3xx10^(3)xx10xx10implies" "DeltaP=3Atm`