Volume-of-a-bubble-is-3-times-larger-when-it-reaches-the-surface-from-the-bottom-of-the-lake-What-is-the-depth-of-the-lake-A-10-m-D-40-m-B-20-m-E-50-m-C-30-m-

Question Number 13695 by Joel577 last updated on 22/May/17

Volume of a bubble is 3 times larger

when it reaches the surface from the bottom

of the lake .

What is the depth of the lake ?

(A) 10 m (D) 40 m

(B) 20 m (E) 50 m

(C) 30 m

Commented by Joel577 last updated on 22/May/17

I use p_{surface} = 1 atm

p_{bottom} . V_{bottom} = p_{surface} . V_{surface}

p_{bottom} . V = 1 . 3 V

p_{bottom} = 3 atm

And now I^{'} m stuck

Commented by mrW1 last updated on 22/May/17

p_{bottom} - p_{surface} = 3 - 1 = 2 atm

= 20 m w a t e r d e p t h

Answered by ajfour last updated on 22/May/17

P_{0} V_{f} = (P_{0} + ρ g h) V_{i}

h = \frac{P_{0} (\frac{V_{f}}{V_{i}} - 1)}{ρ g} a n d a s \frac{V_{f}}{V_{i}} = 3

h = \frac{2 P_{0}}{ρ g} = \frac{2 (1.013 \times 10^{5} N / m^{2})}{(1000 k g / m^{3}) (9.806 m / s^{2})}

h = \frac{202.6}{9.8} m \approx \frac{29}{1.4} m \approx 20 m .

Commented by Joel577 last updated on 22/May/17

t h a n k y o u v e r y m u c h

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