Water is filled in a container upto height 3m. A small hole of area 'a' is punched in the wall of the container at a height 52.5 cm from the bottom. The cross sectional area of the container is A. If `a//A=0.1` then `v^2` is (where v is the velocity of water coming out of the hole)

Options

A. 48
B. 51
C. 50
D. 51.5

Answer

C

Explanation

Applying Burnoulli's theorem between open surface and out let.
`P_(0)+(1)/(2)rhoV^(2)+rhog(h-h_(0))=P_(0)+(1)/(2)rhov^(2)+0`
`V^(2)+2g(h-h_(0))=v^(2)`
From equation of continuity
`AV=av`
`V=(a)/(A)V`
From (1) and (2)
`((a)/(A)v)^(2)+2g(h-h_(0))=v^(2)`
`v^(2)(1-((a)/(A))^(2)]=2g(h-h_(0))impliesv^(2)=(2g(h-h_(0)))/(1-((a)/(A))^(2))`
`v^(2)=(2xx10(3-0.525))/(1-(0.1)^(2))" "impliesv^(2)=50`