Question

A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the Bulk modulus of the ball material? (Take density of water = 1000 kg/m${}^3$):

• 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 $19.6\times {10}^{8}N/m^2$

$\frac{\Delta V}{V}=\frac{0.1}{100},$

$p=h\rho g=200\times 1000\times 9.8$

$=19.6\times {10}^5$

$K=\frac{P}{\frac{\Delta V}{V}}=\frac{19.6\times {10}^5}{\frac{0.1}{100}}=19.6\times {10}^5\times {10}^3$

$=19.6\times {10}^{8}N/m^2$