The volume of a material reduces by $2 \%$ when the pressure is increased from $1 \mathrm{~atm}$ to 2 atm. What is it's bulk modulus?

• A

  $10^5 \mathrm{~N} / \mathrm{m}^2$
• B

  $5 \times 10^5 \mathrm{~N} / \mathrm{m}^2$
• C

  $10^6 \mathrm{~N} / \mathrm{m}^2$
• Correct answer
  D

  $5 \times 10^6 \mathrm{~N} / \mathrm{m}^2$

Solution

By using the equation of Bulk modulus
It is given that $\frac{\Delta V}{V}=2 \%=-\frac{2}{100}$ As we know that, [ - ve sign shows that volume is reduced by increasing pressure.] Let $p$ be the pressure difference. i.e. $p=2 \mathrm{~atm}-1 \mathrm{~atm}=1 \mathrm{~atm}=1.01 \times 10^5 \mathrm{~N} / \mathrm{m}^2$ Now, Bulk modulus, $B=\frac{1.01 \times 10^5 \times 100}{2} \mathrm{~N} / \mathrm{m}^2$ $$ \begin{aligned} B & =5.05 \times 10^6 \mathrm{~N} / \mathrm{m}^2 \\ & \approx 5 \times 10^6 \mathrm{~N} / \mathrm{m}^2 \end{aligned} $$

Hence, the correct answer is option: 'D'.