Question

A ball falling in a lake of depth $200m$ shows $0.1$% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball:

• A. $19.6\times {10}^{8}N/m^2$
• B. $19.6\times {10}^{-10}N/m^2$
• C. $19.6\times {10}^{10}N/m^2$
• D. $19.6\times {10}^{-8}N/m^2$

Answer 1

The correct option is A $19.6\times {10}^{8}N/m^2$

Change in pressure $\Delta P=\rho gh=1000\times 9.8\times 200=1.96\times {10}^{6}Pa$

Fraction of change in volume $\frac{\Delta V}{V}=0.001$

Bulk modulus $B=\frac{\Delta P}{\Delta V/V}=\frac{1.96\times {10}^6}{0.001}=19.6\times {10}^{8}N/m^2$