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The diagram shows the stress-strain graphs of two different materials A and B. Two rods A and B, made of materials A and B respectively have same length and cross sectional area. The rods are subjected to same tensile force. Total elastic potential energy stored in A is $U_{1}$ and that stored in B is $U_{2}$ . Then

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$U_{1} > U_{2}$

$U_{1} < U_{2}$

$U_{1} = U_{2}$

Relation between $U_{1} and U_{2}$ cannot be determined as information is not sufficient.

answer is B.

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Detailed Solution

From the given diagram, it is clear that $Y_{A} > Y_{B}$ . Also, stress $(σ)$ developed in A and B are the same. The rods have same volume.

Now elastic potential energy per unit volume

$u = \frac{σ^{2}}{2 Y} and U = \frac{σ^{2}}{2 Y} x volume .$

Since $Y_{A} > Y_{B}$ , we can conclude $U_{1} < U_{2}$

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