Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

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

$\frac{P}{B}$

$\frac{B}{3P}$

$\frac{3P}{B}$

$\frac{P}{3B}$

Bulk Modulus Formula: The Bulk Modulus ( $B$ ) is defined as the ratio of hydraulic stress (pressure $P$ ) to the volumetric strain ( $\frac{\Delta V}{V}$ ). Considering magnitude: $B = \frac{P}{\frac{\Delta V}{V}} \implies \frac{\Delta V}{V} = \frac{P}{B}$ (Reference: )
Volume-Radius Relationship: The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$ .
Fractional Change: For small changes, the fractional change in volume is three times the fractional change in radius: $\frac{\Delta V}{V} = 3 \frac{\Delta r}{r}$
Substitution: Substitute the expression for volumetric strain into the Bulk Modulus equation: $3 \frac{\Delta r}{r} = \frac{P}{B}$ $\frac{\Delta r}{r} = \frac{P}{3B}$

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