Water is filled in a container up to height `3 m`. 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. ` 50 m^2//s ^ 2 `
B. `51 m^2// s ^ 2 `
C. `48 m^ 2//s ^ 2 `
D. `51.5 m ^ 2//s^ 2 `

Answer

A

Explanation

Using Bernoulli’s theorem
`rArrP_(0)+rhogh+(1)/(2)rhov_(1)^(2)`
`=P_(0)+(1)/(2)rhov_(2)^(2)" "...(i)`
`"Using" Av_(1)=av_(2)" "...(ii)`
`v^(2)=(2gh)/(sqrt(1-((a)/(A))^(2)))=(2xx10xx2.475)/(sqrt(1-(0.1)^(2)))=50m^(2)//s^(2)`