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MHT CET 2025 (20 Apr, Shift 2) · Pressure in a Fluid

Pressure in a Fluid question from MHT CET 2025 (20 Apr, Shift 2)

Q7MHT CET 2025 · 20 APR · SHIFT 2Medium

Pressure in a Fluid

The temperature of an air bubble while rising from bottom to surface of a lake remains constant but diameter is doubled. If pressure on the surface is $h$ meter of mercury column and relative density of mercury is ' $\rho$ ' then the depth of the lake is

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Answer: (b)

Diameter doubles, so volume becomes 8 times. Boyle's law: $P_{bottom}V = P_{surface}(8V)$ , so $P_{bottom} = 8P_{surface}$ .
Surface pressure $h$ m of mercury $= h\rho$ m of water.
$h\rho + d = 8h\rho \Rightarrow d = 7h\rho$
So the answer is (b) $7h\rho$ .

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