A bubble of gas released at the bottom of a lake increases to eight times its original volume when it reaches the surface. Assuming that atmospheric pressure is equivalent to the pressure exerted by a column of water 10 m height, the depth of the lake is

Options

A. 80m
B. 90m
C. 40m
D. 70cm

Answer

D

Explanation

Let the depth of lake is h, water density is `rho` , gravity is g and volume of bubble at bottom of lake is V . Applying Boyle’s law :
Pressure x volume at the surface = Pressure x volume at the bottom of the lake
`(10m xx rho xx g) xx 8V = {(h+10)m xx rho xx g} xx v `
`h + 10 = 80m. rArr h= 70m`