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JEE Main 202529 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2025 · 29 January · Morning Shift · Physics · Mechanical Properties of Solids

The fractional compression ( ( Δ V V ) of water at the depth of 2.5...

The fractional compression ((ΔVV)\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right) of water at the depth of 2.5 km below the sea level is ______ (\%). Given, the Bulk modulus of water (=2 ×\times10^9  N m−2\mathrm{~N} \mathrm{~m}^{-2}, density of water =103=10^3 (kg\mathrmm−3\mathrm{kg} \mathrmm^{-3}, acceleration due to gravity (=g=\mathrm{g}=10  m s−2\mathrm{~m} \mathrm{~s}^{-2}.

Options

  1. A1.25
  2. B1.0
  3. C1.75
  4. D1.5

Correct answer

A. 1.25

Step-by-step solution

B=ρgh(Δvv)Δvv×100=ρghB×1001000×10×2.5×1032×109×100%=1.25%\begin{aligned} & \mathrm{B}=\frac{\rho \mathrm{gh}}{\left(\frac{\Delta \mathrm{v}}{\mathrm{v}}\right)} \\ & \frac{\Delta \mathrm{v}}{\mathrm{v}} \times 100=\frac{\rho \mathrm{gh}}{\mathrm{B}} \times 100 \\ & \frac{1000 \times 10 \times 2.5 \times 10^3}{2 \times 10^9} \times 100 \% \\ & =1.25 \%\end{aligned}
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