NEET Physics Question - Solid and Fluids

The bulk modulus of a spherical objects is '$B$'. If it is subjected to uniform pressure '$P$', the fractional decrease in radius is:

(2017-Delhi)

$\frac{B}{3P}$

$\frac{3P}{B}$

$\frac{P}{3B}$

$\frac{P}{B}$

Solution:

Bulk modulus $B = \frac{P}{\Delta V/V} \Rightarrow \frac{\Delta V}{V} = \frac{P}{B}$. For a sphere, $V = \frac{4}{3}\pi r^3$, so the fractional change in volume is $\frac{\Delta V}{V} = 3 \frac{\Delta r}{r}$. Therefore, $$\frac{\Delta r}{r} = \frac{1}{3} \frac{\Delta V}{V} = \frac{P}{3B}$$.

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