Question

a sphere contracts in volume by 0.01℅ when taken to the bottom of a sea 1km deep.Find the bulk modulus of the material of the sphere.Density of sea water may be taken as 1000kg/cubic metre.

Answer 1

Pressure under the at a depth 1km = $P_{atm}+h$ρ$g$

Since atmospheric pressure is comparatively low we can neglect it.

Pressure under 1km (1000m) = $1000 \times 1000 \times 10 = 10^{7} kg/m^{2}$ (taking g=10 m/s²)

Bulk modulus = (F/A)/(ΔV/V) = P/(ΔV/V) = $\frac{10^7}{0.0001} = 10^{11} kg/m^{2}$

(We have given change in volume in %. (ΔV/V)x100 = 0.01 ⇒ΔV/V = 0.0001)