First slide

Elastic Modulie

Question

If a pressure ‘p’ is applied normal to a wire of Young's modulus Y, the energy stored per unit volume is:

Moderate

A

$\frac{1}{2} p^{2} Y$
B

$\frac{1}{2 Y} p^{2}$
C

$\frac{1}{2} {pY}^{2}$
D

$\frac{1}{2} pY$

Solution

The energy stored per unit volume is
U = $\frac{1}{2} stress \times strain$
= $\frac{1}{2} stress \times \frac{s t r e s s}{Y}$
U = $\frac{{(stress)}^{2}}{2 Y} = \frac{P^{2}}{2 Y}$
So the correct choice is (2).

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