The bulk modulus of a spherical object is '$B$'. If it is subjected to uniform pressure '$P$', the fractional decrease in radius is
NEET 2017, Medium
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Bulk modulus $B$ is given as
$B = \frac{{ - pV}}{{\Delta V}}$ $...(i)$
The volume of a spherical object of radius $r$ is given as
$V = \frac{4}{3}\pi {r^3}\,\,,\,\,\Delta V = \frac{4}{3}\pi \left( {3{r^2}} \right)\Delta r$
$\therefore - \frac{V}{{\Delta V}} = \frac{{\frac{4}{3}\pi {r^3}}}{{\frac{4}{3}\pi 3{r^2}\Delta r}}\,\,or\,\, - \frac{V}{{\Delta V}} = - \frac{r}{{3\Delta r}}$
Put this value in eqn. $(i)$, we get
$B = - \frac{{pr}}{{3\Delta r}}$
Fractional decrease in radius is
$ - \frac{{\Delta r}}{r} = \frac{p}{{3B}}$
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