Question

When a pressure of 100 atmosphere is applied on a spherical ball of rubber, then its volume reduces to $0.01\%$. The bulk modulus of the material of the rubber in $\frac{dyne}{c{m}^2}$ is

• A. $10\times {10}^{12}$
• B. $100\times {10}^{12}$
• C. $1\times {10}^{12}$
• D. $20\times {10}^{12}$

Answer 1

The correct option is C $1\times {10}^{12}$

1 atm = ${10}^5\frac{N}{m^2}$ $\therefore 100atm={10}^7\frac{N}{m^2}$ and $\Delta V=0.01\%V$ $\therefore \frac{\Delta V}{V}=0.0001$
$K=\frac{P}{\frac{\Delta V}{V}}=\frac{{10}^7}{0.0001}=1\times {10}^{11}\frac{N}{m^2}=1\times {10}^{12}\frac{Dyne}{c{m}^2}.$