An aluminum ball is subjected to a pressure of $7.00 \times 10^{6} \mathrm{~Pa}$. The volume strain is $-1.0 \times 10^{-4}$. What is the bulk modulus?
A) $8.1 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
B) $6.3 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
C) $5.8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
D) $7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
E) $6.1 \times 10^{10}\mathrm{~N} / \mathrm{m}^{2}$

Question

Quizplus · Accepted Answer

The bulk modulus (K) is defined as the ratio of pressure applied to the volume strain it produces, $K = \frac{P}{\text{Volume Strain}}$. Given $P = 7.00 \times 10^{6} \mathrm{~Pa}$ and Volume Strain = $-1.0 \times 10^{-4}$, $K = \frac{7.00 \times 10^{6}}{-1.0 \times 10^{-4}} = -7.0 \times 10^{10} \mathrm{~N/m}^{2}$. The negative sign indicates a reduction in volume, but when considering the magnitude for bulk modulus, we take the absolute value, hence $7.0 \times 10^{10} \mathrm{~N/m}^{2}$.

An Aluminum Ball Is Subjected to a Pressure Of 7.00×106 Pa7.00 \times 10^{6} \mathrm{~Pa}7.00×106 Pa

An Aluminum Ball Is Subjected to a Pressure Of $7.00 \times 10^{6} \mathrm{~Pa}$