Question

A sphere contracts in volume by 0.02% when taken to the bottom of sea 2 km deep. Find the value of bulk modulus of the material of sphere. Density of sea water = 1 g/cc, g = 10m/s^-2

Answer 1

\(\frac{\Delta V}{V}\) = 0.02% =\(-\frac{0.02}{100}\)

h = 2 km = 2 x 1000 m = 2000 m

Density of sea water (ρ) = 1 g/cc = 1000 kg/m³

Pressure applied:

P = hρg

= 2000 x 10³ x 10

= 2 x 10⁷ N/m²

Bulk modulus \(\beta = -\frac{P}{\frac{\Delta V}{V}}\)

\( =\frac{2\times10^7}{-\frac{0.02}{100}}\) = 10¹¹ N/m²

Modulus of Rigidity