A cubical solid aluminium (bulk modulus ) 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 and , respectively, the cha

Question

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 $10^{3} {kg m}^{- 3}$ and $10 {m s}^{- 2}$ , respectively, the change in the edge length of the block in mm is ______. [2020]

Smart Achievers · Accepted Answer

(0.24)

$As we know, bulk modulus B = \frac{P}{(- \frac{d V}{V})}$

$\Rightarrow \frac{d V}{V} = - \frac{P}{B} \Rightarrow 3 (\frac{Δ ℓ}{ℓ}) = - \frac{P}{B}$

$Δ ℓ = (\frac{- P}{B}) \frac{ℓ}{3} = (\frac{ρ g h}{B}) \frac{ℓ}{3}$

$= \frac{10^{3} \times 10 \times 5 \times 10^{3}}{70 \times 10^{9}} \times \frac{1}{3} = 0.238 \times 10^{- 3}$

$∴$ $Δ ℓ = 0.238 mm ≃ 0.24 mm$

Solution

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Solution

Ans. (0.24) As we know, bulk modulus B=P(-dVV) ⇒dVV=-PB⇒3(Δℓℓ)=-PB Δℓ=(-PB)ℓ3=(ρghB)ℓ3 =103×10×5×10370×109×13=0.238×10-3 ∴ Δℓ=0.238 mm≃0.24 mm

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