First slide

Elastic Modulie

Question

The ratio of young's modulus of elasticity (Y) to the bulk modulus of elasticity of a material is 1.8. If the length of a rod of uniform cross sectional area made of thin material is increased by 0.04% under the action of a tensile force, then its diameter changes by

Moderate

A

0.008%, decrease
B

0.08%, increase
C

0.006%, increased
D

0.06%, decrease

Solution

$\begin{array}{l} Y = 3 K (1 - 2 μ) \\ \Rightarrow μ = \frac{1}{2} (1 - \frac{Y}{3 K}) = \frac{1}{2} (1 - \frac{1.8}{3}) = 0.2 \\ ∴ \frac{Δ d}{d} = - μ \frac{Δ l}{l} = - 0.2 \times 0.04 % = - 0.008 % \end{array}$

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