First slide

Stress and strain

Question

Strain energy B stored in unit volume of a rod of diameter ‘d’, subjected to tensile force is ‘u’. Then the strain energy stored in unit volume of a rod of diameter ‘2d’, made of same material and subjected to same tensile force, will be

Moderate

A

u / 8
B

u / 16
C

2u
D

4u

Solution

$\begin{array}{l} Stress = σ = \frac{4 F}{{πd}^{2}} and u = \frac{σ^{2}}{2 Y} = \frac{8 F^{2}}{π^{2} d^{4} Y} \\ σ' = \frac{4 F}{π {(2 d)}^{2}} = \frac{F}{{πd}^{2}} and u' = \frac{{(σ')}^{2}}{2 Y} = \frac{F^{2}}{2 π^{2} d^{4} Y} \\ ∴ \frac{u'}{u} = \frac{1}{16} \Rightarrow u' = \frac{u}{16} \end{array}$

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