An air bubble doubles its radius on raising from the bottom of water reservoir t

Discussion Forum : Kinetic Theory Of Gases

Question - An air bubble doubles its radius on raising from the bottom of water reservoir to be the surface of water in it. If the atmospheric pressure is equal to 10 m of water, the height of water in the reservoir is

Options:

A . 10 m

B . 20 m

C . 70 m

D . 80 m

Answer: Option C
:
C
Accoding to Boyle's law

(P_{1} V_{1})_{b o t t o m}

(P_{2} V_{2})_{t o p}

(10 + h)

\times

\frac{4}{3} π {r_{1}}^{3}

= 10

\times

\frac{4}{3} π {r_{2}}^{3}

but

r_{2} = 2 r_{1}

∴

(10 + h)

{r_{1}}^{3}

= 10

\times

{r_{1}}^{3}

∴

10 + h = 80

∴

h = 70 m

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