JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Elasticity & SHM

A cubical solid aluminium (bulk modulus

= - V \frac{d P}{d V} = 70

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

1 0^{3} kg m^{- 3}

and

10 ms^{- 2}

, respectively, the change in the edge length of the block in mm is ____.

Answer: 0.24

Solution

Bulk modulus:

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

For a cube:

\frac{d V}{V} = 3 \frac{d a}{a}

Pressure at depth h:

Δ P = ρ g h = 1 0^{3} \times 10 \times 5000 = 5 \times 1 0^{7}

B = - \frac{V Δ P}{Δ V} = - \frac{a Δ P}{3Δ a}

70 \times 1 0^{9} = \frac{1 \times 5 \times 1 0 ^{7}}{3∣Δ a ∣}

∣Δ a ∣ = \frac{5 \times 1 0 ^{7}}{3 \times 70 \times 1 0 ^{9}} = \frac{5}{210 \times 1 0 ^{2}} = \frac{1}{4200}

= \frac{1 0 ^{3}}{4200}

= \frac{5}{21}

\approx 0.238

\approx 0.24

JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Numerical answer

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JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Elasticity & SHM

Solution

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