Elastic behaviour of solids

Question

A copper bar of length L and area of cross section A is placed in a chamber at atmospheric pressure. If the chamber is evacuated, the percentage change in its volume will be (compressibility of copper is $8 \times 10^{- 12} m^{2} / N$ and 1 atm = 10⁵ N/m)

Moderate

A

$8 \times 10^{- 7}$
B

$8 \times 10^{- 5}$
C

$1.25 \times 10^{- 4}$
D

$1.25 \times 10^{- 5}$

Solution

$\frac{1}{K} = \frac{ΔV / V}{ΔP} or \frac{ΔV}{V} = ΔP (\frac{1}{K})$
$or \frac{ΔV}{V} \times 100 = 10^{5} \times 8 \times 10^{- 12} \times 100 = 8 \times 10^{- 5}$

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