The diameter of an air-bubble formed at the bottom of a pond is `d=4mum`, when the bubble rises to the surface, its diameter increases `n=1.1` times. If expansion of air bubble is assumed to be isothermal and atmospheric pressure to be standard. How deep the pond at the spot is [surface tension of water `0.075(N)/(m)`]

Explanation

By Boyle's law
`(p_0 + h g rho + (4 alpha)/(d))(pi)/(6) d^3 = (p_0 +m (4 alpha)/(nd)) (pi)/(6)n^3 d^3`
or `[hg rho - p_0 (n^3 - 1)] = (4 alpha)/(d) (n^2 - 1)`
or `h = [p_0 (n^3 - 1) + (4 alpha)/(d) (n^2 - 1)]//g rho = 4.98` meter of water.