An air bubble rises from the bottom of a water tank of height 5 m. If the initial volume of the bubble is `3" mm"^(3)`, then what will be its volume as it reaches the surface? Assume that its temperature does not change.
`[g=9.8m//s^(2),1" atm "=10^(5)” Pa, density of water"=1" gm"//"cc"]`

Options

A. `1.5" mm"^(3)`
B. `4.5" mm"^(3)`
C. `9" mm"^(3)`
D. `9" mm"^(3)`

Answer

B

Explanation

Using
`((p_(a)+rho gh)r_(1)^(3))/(T_(1))=(p_(a)r_(2)^(3))/(T_(2))`
`because" "T_(1)=T_(2)`
`:." "r_(2)^(3)=(1)/(p_(a))(p_(a)+rho gh)r_(1)^(3)`
Using all values in SI system,
`r_(2)^(3)=(1)/(10^(5))[10^(5)+10^(3)xx9.8xx5]r_(1)^(3)`
`r_(2)^(3)~~1.5r_(1)^(3)`
`implies" "(4)/(3)pi r_(2)^(3)~~(1.5)(4)/(3)pi r_(1)^(3)`
`V_(2)=1.5xxV_(1)`
`implies" "V_(2)=1.5xx3=4.5" mm"^(3)`