When a large bubble rises from the bottom of a lake to the surface, its radius doubles, The atmospheric pressure is equal to that of a column of water of height H. The depth of the lake is

Options

A. `30 m`
B. `40 m`
C. `70m `
D. ` 80 m `

Answer

C

Explanation

Assuming constant temperature.
`P_1 V_1 = P_2 V_2 " "(P_0 + rho gh ) 4/3 pi r^3 = p_0 xx 4/3 pi (2 r)^2`
` p_0 + rho gh = B P_0 rArr rho gh = 7 P_0`
Given `P_0 = 10 rho g`
So `rho gh = 7xx10 rho g rArrh = 70 m`