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

Answer: (A)

The bulk modulus $ B=\frac{\Delta p}{\Delta V/V}=\frac{h\rho g}{0.1/100} $ $ =\frac{200\times {{10}^{3}}\times 9.8}{1/1000} $ $ =19.6\times {{10}^{8}}N/{{m}^{2}} $