Physics · Mechanical Properties of Matter

JEE Advanced 2020 — Paper 2 — Question 14

A cubical solid aluminium (bulk modulus $=-V \frac{\mathrm{dP}}{\mathrm{dV}}=70 \mathrm{GPa}$ ) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be $10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ and $10 \mathrm{~ms}^{-2}$ , respectively, the change in the edge length of the block in mm is $\_\_\_\_$

Answer: 0.238

Numerical answer — enter this value.

Step-by-step solution

$B=-V \frac{d P}{d V}$

$70 \times 10^{9}=\frac{(1)^{3} \times 5 \times 10^{3} \times 10}{\Delta V}$

$\Rightarrow \Delta \mathrm{V}=\frac{5}{7} \times 10^{-3}$

$\Rightarrow \frac{\Delta \mathrm{V}}{\mathrm{V}}=\frac{3 \Delta \ell}{\ell}$

$\Rightarrow \Delta \ell=\frac{5}{21}=0.238 \mathrm{~mm}$

Answer key and solution verified before publishing.

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Exam: JEE Advanced 2020
Paper: Paper 2
Subject: Physics
Chapter: Mechanical Properties of Matter
Topic: Stress,Strain and Modulus of Elasticity