The bulk modulus of a spherical object is 'B' | vedclass

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Question

(B) Bulk modulus $B$ is defined as $B = -\frac{P}{\Delta V / V}$,where $\Delta V / V$ is the volumetric strain.The volume of a sphere is $V = \frac{4}

Vedclass · Accepted Answer

$\frac{P}{3B}$

Vedclass · Answer

(B) Bulk modulus $B$ is defined as $B = -\frac{P}{\Delta V / V}$,where $\Delta V / V$ is the volumetric strain.The volume of a sphere is $V = \frac{4}{3} \pi r^3$.Differentiating with respect to $r$,we get $\Delta V = 4 \pi r^2 \Delta r$.The volumetric strain is $\frac{\Delta V}{V} = \frac{4 \pi r^2 \Delta r}{\frac{4}{3} \pi r^3} = 3 \frac{\Delta r}{r}$.Substituting this into the bulk modulus formula:$B = -\frac{P}{3 \Delta r / r}$.Rearranging for the fractional decrease in radius $(-\frac{\Delta r}{r})$:$-\frac{\Delta r}{r} = \frac{P}{3B}$.

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

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