Question

In rising from the bottom of a lake to the top, the temperature of air bubble remains unchanged, but the diameter gets doubled. If $h$ is the barometric height (expressed in metres of mercury of relative density $\rho$) at surface of the lake, the depth of the lake (in metres) is

• A. $8\rho h$
• B. $4\rho h$
• C. $7\rho h$
• D. $2\rho h$

Answer 1

The correct option is C $7\rho h$

Temperature constant => PV= constant,
The volume is 8 times as diameter gets doubled. pressure gets 1/8 times
air pressure*8 = air pressure + pressure due to water
=>height due to water $=7\rho h$