A bubble is at the bottom of the lake of depth h . As the bubble...

A bubble is at the bottom of the lake of depth $h$ . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to $l$ metre of water column, then $h$ is equal to

Options

A $26l$
B $l$
C $25l$
D $30l$

Correct answer

A. $26l$

Step-by-step solution

From Boyle's law

pV =

constant

∴ {p}_{1}{V}_{1} = {p}_{2}{V}_{2}

Here,

{p}_{1} = ρg\left(h + l\right), {V}_{1} = \dfrac{4}{3}\pir^{3}

{p}_{2} = ρgl, {V}_{2} = \dfrac{4}{3}\pi ( 3{r )}^{3}

∴ \left(h + l\right)\dfrac{4}{3}\pir^{3} = l \times \dfrac{4}{3}\pi{\left(3r\right)}^{3}

h + l = 27l

∴ h = 26l

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