First slide

Elastic Modulie

Question

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

Moderate

A

$\frac{B}{3 p}$
B

$\frac{3 p}{B}$
C

$\frac{p}{3 B}$
D

$\frac{p}{B}$

Solution

$B = \frac{∆ P}{- \frac{∆ V}{V}}, \frac{∆ V}{V} = \frac{3 ∆ R}{R}$
$B = \frac{∆ P}{- \frac{3 ∆ R}{R}} \Rightarrow - \frac{∆ R}{R} = \frac{P}{3 B} (∆ P = P)$

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