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PhysicsNumerical+4Question 16 of 54

JEE Advanced 2020 · Paper 2, Physics question 16

A cubical solid aluminium (bulk modulus =−VdPdV=70= -V\dfrac{dP}{dV} = 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 103 kg m−310^3\ \mathrm{kg\,m^{-3}} and 10 m s−210\ \mathrm{m\,s^{-2}}, respectively, the change in the edge length of the block in mm is ______.

Answer and worked solution

Official answer: 0.23

Pressure at the bottom.
ΔP=ρgh=103×10×5000=5×107 Pa.\Delta P=\rho gh=10^3\times10\times5000=5\times10^7\text{ Pa}.

Strains.
ΔVV=ΔPB=5×1077×1010=7.14×10−4,ΔLL=13ΔVV=2.38×10−4.\frac{\Delta V}V=\frac{\Delta P}B=\frac{5\times10^7}{7\times10^{10}}=7.14\times10^{-4},\qquad\frac{\Delta L}L=\frac13\frac{\Delta V}V=2.38\times10^{-4}.

The edge shrinks by 2.38×10−42.38\times10^{-4} m, about 0.24 mm.

Answer: −0.24 (a decrease; the key accepts 0.23 to 0.25 or −0.25 to −0.23)

Topics:Hooke's law and elastic moduliPressure and Pascal's law
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