Question

To what depth must a rubber ball be taken in deep sea so that its volume is decreased by 0.1%. (The bulk modulus of rubber is 9.8 × 10⁸ Nm^-2, and the density of sea water is 10³ kgm^-3.)

Answer 1

Bulk Modulus, K = 9.8 × 10⁸ N/m²

Density of sea water (ρ) = 10³Kg/m³

Volume decrease (Percentage)

(\(\frac{∆V}{V}\) × 100) = 0.1

\(\frac{∆V}{V}\) = \(\frac{0.1}{100}\)

= \(\frac{1}{100}\) = 1 × 10⁻³

Let rubber ball be taken up to depth h

∴ Change in pressure P = hpg

Bulk Modulus,

B = \(\bigg|\frac{P}{\frac{∆V}{V}}\bigg|\) = \(\frac{hpg}{\frac{∆V}{V}}\)

Or, h = \(\frac{B\times(\frac{∆V}{V})}{pg}\)

= \(\frac{9.8×10^8×1×10^{−3}}{10^3×9.8}\)

h = 100 m