Question

A cube of metal is subjected to a hydrostatic pressure of $4\text{GPa}$. The percentage change in the length of the side of the cube is close to :(Given bulk modulus of metal, $B=8\times {10}^{10}\text{Pa})$

• A. $5$
• B. $0.6$
• C. $20$
• D. $1.67$

Answer 1

The correct option is D $1.67$

Bulk modulus, $B=\frac{P}{\frac{dV}{V}}$
$\Rightarrow \frac{dV}{V}=\frac{P}{B}.....\left(i\right)$

If the side of cube is $L$, then,
$V=L^3$
Differentiating both sides, we get, $dV=3L^{2}dL$

$\therefore \frac{dV}{V}=\frac{3dL}{L}=\frac{P}{B}$

$\Rightarrow \frac{dL}{L}=\frac{1}{3}\times \frac{P}{B}$

$=\frac{4\times {10}^9}{3\times 8\times {10}^{10}}=\frac{1}{60}$

$\Rightarrow \frac{dL}{L}\times 100=\frac{1}{60}\times 100=1.67$%.

Hence, $\left(D\right)$ is the correct answer.