First slide

Elastic Modulie

Question

If compressibility of a material is 4 X 10^-5 per atm, pressure is 100 atm and volume is 100 cm³ , then find the value of $Δ V$ . [JIPMER 2018]

Moderate

A

0.4 cm³
B

0.8 cm³
C

0.6 cm³
D

0.2 cm³

Solution

Given,    $k = 4 \times 10^{- 5} per atm$
   $p = 100 atm$
and    $V = 100 {cm}^{3}$
$= 100 \times 10^{- 6} m^{3}$
$∵ Compressibility = \frac{1}{∣ Bulk modulus of elasticity ∣}$
$k = \frac{1}{Δ p \frac{V}{Δ V}} = \frac{Δ V}{Δ p V}$
$∴ Δ V = k (Δ p V) = 4 \times 10^{- 5} (100 \times 100 \times 10^{- 6})$
$= 0.4 \times 10^{- 6} m^{3} = 0.4 {cm}^{3}$

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