A steel ball with a diameter of $10 \mathrm{~cm}$ is subjected to a pressure that causes the volume of the ball to shrink by $0.01 \%$. The bulk modulus for steel is $1.6 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}$. What is the pressure?
A) $1.6 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
B) $2.4 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
C) $1.2 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
D) $1.9 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
E) $2.1 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$

Question

Quizplus · Accepted Answer

The pressure can be calculated using the formula for bulk modulus, $B = -\frac{\Delta P}{\Delta V / V}$, where $\Delta P$ is the pressure, $\Delta V / V$ is the fractional change in volume, and $B$ is the bulk modulus. Given that the volume shrinks by $0.01\%$, $\Delta V / V = -0.0001$. Substituting the given bulk modulus, $B = 1.6 \times 10^{11} \mathrm{~N/m^2}$, we find $\Delta P = B \times \Delta V / V = 1.6 \times 10^{11} \times -0.0001 = 1.6 \times 10^{7} \mathrm{~N/m^2}$.

A Steel Ball with a Diameter Of 10 cm10 \mathrm{~cm}10 cm Is Subjected to a Pressure That Causes the Volume of Subjected

A Steel Ball with a Diameter Of $10 \mathrm{~cm}$ Is Subjected to a Pressure That Causes the Volume of Subjected