Question

Fractional change in the radius of a sphere of bulks modulus $B$, when it is compressed by pressure $P$ from all sides is

• A. $\frac{4P}{3B}$
• B. $\frac{3P}{B}$
• C. $\frac{P}{B}$
• D. $\frac{P}{3B}$

Answer 1

The correct option is D $\frac{P}{3B}$

$B=\frac{P}{\frac{\Delta V}{V}}\Rightarrow \frac{\Delta V}{V}=\frac{P}{B}$

$V=\frac{4}{3}\pi R^3\Rightarrow \Delta V=4\pi R^2\Delta R\Rightarrow \frac{\Delta V}{V}=\frac{3\Delta R}{R}$

So $\frac{\Delta R}{R}=\frac{P}{3B}$