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when an air bubble rises from the bottom...

when an air bubble rises from the bottom to the surface of a lake, its radius becomes double . Find the depth of the lake , given that the atmospheric pressure is equal to the pressure due to a column of water 10 m high. Assume constant temperature and disreged surface tension .

A

`30 m`

B

`40 m`

C

`70m `

D

` 80 m `

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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