JEE Main 2025 Jan 29 Shift 1, Physics Q13: Properties of Fluids

JEE Main2025Jan 29, Shift 1Physics

The fractional compression $(\frac{Δ V}{V})$ of water at the depth of $2.5 km$ below the sea level is _______ %.

Given, the Bulk modulus of water $= 2 \times 1 0^{9} N m^{- 2}$ , density of water $= 1 0^{3} kg m^{- 3}$ , acceleration due to gravity $= g = 10 m s^{- 2} .$

A
$1.75$
B
$1.0$
C
$1.5$
D
$1.25$

Solution

The hydrostatic pressure at depth $h$ is $P = ρ g h .$ By the definition of bulk modulus $B = - \frac{P}{Δ V / V}$ , ignoring the sign for magnitude:

$\frac{Δ V}{V} = \frac{ρ g h}{B} = \frac{1 0 ^{3} \cdot 10 \cdot 2.5 \times 1 0 ^{3}}{2 \times 1 0 ^{9}} = 1.25 \times 1 0^{- 2} .$

Expressed as a percentage: $1.25%.$

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JEE Main 2025 Jan 29 Shift 1, Physics Q13: Properties of Fluids

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