When an air bubble of radius r rises from the bottom (the to the surface of a lake. Its radius becomes `(5r)/4` pressure of the atmosphere is equal to the 10 m height of water column). If the temperature is constant and the surface tension is neglected the depth of the lake is

Options

A. 5.53m
B. 6.53m
C. 9.53m
D. 12.53m

Answer

C

Explanation

`P_(1)=hdg + h_(1)dg`,
`P_(1)V_(1) = P_(2)V_(2)`
`dg (10+h) xx 4/3 pi r_(1)^(2) = hdg xx 4/3 pi r_(2)^(3)`
`therefore h = 1250/64 - 10 = 610/64 = 9.53m`