Question

A sphere contracts in volume by 0.01% when taken to the bottom of sea 1 km deep. If the density of sea water is 10^3 kg m^−3 , find the bulk modulus of
the material of the sphere.

Answer 1

Let the bulk modulus be B. The initial volume be V and the final volume is (V)(0.1/100) = 0.001V

Change in volume is, dV = 0.001V – V = -0.999V

Pressure on the body, P = ρgh = (1000 kg/m3)(9.8 m/s2)(500 m) = 4900000 Pa

Now,

B = -P/(dV/V)

=> B = -4900000/(-0.999V/V)

=> B = 4.9 × 106 Pa