Question

A spherical ball contracts in volume by 0.0098% when subjected to a pressure of 100 atm. Calculate its bulk modulus. Given 1 atm = 1.01 x ${10}^{5}N{m}^{-2}$.

• A. 1.033 x ${10}^{7}N{m}^{-2}$)
• B. 1.066 x ${10}^{5}N{m}^{-2}$)
• C. 1.033 x ${10}^{11}N{m}^{-2}$)
• D. 1.021 x ${10}^{6}N{m}^{-2}$)

Answer 1

The correct option is C 1.033 x ${10}^{11}N{m}^{-2}$)

$\begin{array}{c}\text{Given Contraction in volume}\frac{\Delta v}{v}=0.0098\%\\ \text{pressure}=100\text{atm}\\ \text{l atm}=1.01\times {10}^5{Nm}^{-2}\end{array}$

$\begin{array}{c}\text{We know that Bulk modulus}=\frac{p}{\frac{\Delta v}{v}}\\ B=\frac{\text{100 atm}}{\frac{0.0098}{100}}\\ =\frac{{10}^2\times {10}^2\times 1.01\times {10}^5}{98\times {10}^{-4}}\end{array}$

$B=1.033\times {10}^{11}{Nm}^{-2}$