The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of $7 \times 10^{6} \mathrm{~Pa}$, would be ______ $\mathrm{mm}^{3}$. (Given bulk modulus of copper $=1.4 \times 10^{11} \mathrm{Nm}^{-2}$ )

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Elasticity & SHM

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of

7 \times 1 0^{6} Pa

, would be ______

mm^{3}

.
(Given bulk modulus of copper

= 1.4 \times 1 0^{11} Nm^{- 2}

)

Answer: 50

The bulk modulus relates pressure change to fractional volume change:

B = \frac{Δ P}{Δ V / V} ⟹ Δ V = \frac{Δ P \cdot V}{B}

Given edge length 10 cm = 0.1 m, so

V = (0.1)^{3} = 1 0^{- 3} m^{3}

Δ P = 7 \times 1 0^{6} Pa

B = 1.4 \times 1 0^{11} N/m^{2}

Δ V = \frac{7 \times 1 0 ^{6} \times 1 0 ^{- 3}}{1.4 \times 1 0 ^{11}} = \frac{7 \times 1 0 ^{3}}{1.4 \times 1 0 ^{11}} = 5 \times 1 0^{- 8} m^{3}

Converting to mm

^{3}

(1 m

^{3}

1 0^{9}

^{3}

Δ V = 5 \times 1 0^{- 8} \times 1 0^{9} = 50 mm^{3}

JEE Main · 2025 · 28 Jan 2025 · Shift 2 · Integer answer