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Question: The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface...

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be 75 cm of Hg and the density of water to be 1/10 of the density of mercury, the depth of the lake is

A

5 m

B

10 m

C

15 m

D

20 m

Answer

15 m

Explanation

Solution

P1V1=P2V2P _ { 1 } V _ { 1 } = P _ { 2 } V _ { 2 }⇒(HHgρHg+HWρW)V=HHgρHg×3V\left( H _ { H g } \rho _ { H g } + H _ { W } \rho _ { W } \right) V = H _ { H g } \rho _ { H g } \times 3 V

⇒HHgρHg+HWρHg10=3HHgρHgH _ { H g } \rho _ { H g } + H _ { W } \frac { \rho _ { H g } } { 10 } = 3 H _ { H g } \rho _ { H g }

⇒=2×75×10100=15 m= \frac { 2 \times 75 \times 10 } { 100 } = 15 \mathrm {~m}