A cubical solid aluminium (bulk modulus =-V (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 103 kg m -3 and 10 ms -2, respectively, the change in the edge length of the block in mm is .

Question

A cubical solid aluminium (bulk modulus =-V (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 103 kg m -3 and 10 ms -2, respectively, the change in the edge length of the block in mm is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

B =- V ( dP / dV ) 70 × 109=((1)3 × 5 × 103 × 10/Δ V ) ⇒ Δ V=(5/7) × 10-3 ⇒ (Δ V/V)=(3 Δ ℓ/ℓ) ⇒ Δ ℓ=(5/21)=0.238 mm

B=−VdVdP​ 70×109=ΔV(1)3×5×103×10​ ⇒ΔV=75​×10−3 ⇒VΔV​=ℓ3Δℓ​ ⇒Δℓ=215​=0.238mm

$B = - V \frac{d P}{d V}$
$70 \times 1 0^{9} = \frac{( 1 ) ^{3} \times 5 \times 1 0 ^{3} \times 10}{Δ V}$
$\Rightarrow Δ V = \frac{5}{7} \times 1 0^{- 3}$
$\Rightarrow \frac{Δ V}{V} = \frac{3Δ ℓ}{ℓ}$
$\Rightarrow Δ ℓ = \frac{5}{21} = 0.238 mm$