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 dyne $cm ^{-2}$ is

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

Answer 1

Answer: (C)

We know that, $1$ atm $=10^{5} Nm ^{-2}$
$\therefore \,100 \,atm =10^{7} Nm ^{-2}$
and $ \Delta V=0.01 \% V $
$\therefore \frac{\Delta V}{V}=0.0001$
$|B|=\frac{p}{\Delta V / V}=\frac{10^{7}}{0.0001}$
$=1 \times 10^{11} \,Nm ^{-2}$
$=1 \times 10^{12}$ dyne $cm ^{-2}$
$\left[\because 1 N =10^{5}\right.$ dyne $]$