First slide

Elastic Modulie

Question

A spherical ball contracts in volume by 00.01% when subjected to a normal uniform pressure of 100 atmospheres. The bulk modulus of its material in dyne/cm ² is

Easy

A

10 x 10¹²
B

100 x 10¹²
C

1x 10¹²
D

2.0 x 10¹¹

Solution

$B = P / (\frac{ΔV}{V})$
Given that $(ΔV / V) = 0 \cdot 01 % = 0 \cdot 01 \times 10^{- 2}$
$\begin{array}{l} P = 100 \times 1 \cdot 01 \times 10^{5} N / m^{2} \\ = 1 \cdot 01 \times 10^{8} dyne / {cm}^{2} \\ ∴ B = (1 \cdot 01 \times 10^{8}) / (0 \cdot 01 \times 10^{- 2}) \\ \approx 1 \times 10^{12} dynes / {cm}^{2} \end{array}$

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