When an air bubble of radius `'r'` rises from the bottom to the surface of a lake, its radius becomes `5r//4` (the 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. `10.5m`
B. `8.7m `
C. `11.2m`
D. `9.5m`

Answer

D

Explanation

Using `P _(1) V _(1) = P_(2) V _(2)`
` (P_(1)) 4/3 pir ^(3) = (P_(2)) 4/3 pi (125 r ^(3))/(64)`
`(rho g (10 ) + rho g h)/( rho g (10)) = (125)/(64)`
`640 + 64h = 1250`
On solving we get `h = 9.5m`