A metal sphere (bulk modulus of $1 \times 10 ^ { 11 }$ Pa) is put under a hydraulic pressure of $10 ^ { 10 }$ Pa. If the original volume of the sphere was 1 cm $3$ , the new volume of the sphere is
A) 1.2 cm $3$
B) 1.1 cm $3$
C) 0.8 cm $3$
D) 0.9 cm $3$

Question

Quizplus · Accepted Answer

The bulk modulus ($B$) is defined as $B = -\frac{\Delta P}{\Delta V/V}$, where $\Delta P$ is the change in pressure and $\Delta V/V$ is the fractional change in volume. Rearranging this formula to solve for the new volume ($V'$), we get $V' = V(1 - \frac{\Delta P}{B})$. Substituting the given values, $V' = 1 \times (1 - \frac{10^{10}}{10^{11}}) = 1 \times (1 - 0.1) = 0.9$ cm$^3$.

A Metal Sphere (Bulk Modulus Of 1×10111 \times 10 ^ { 11 }1×1011

A Metal Sphere (Bulk Modulus Of $1 \times 10 ^ { 11 }$