Two rods of same dimensions are made of two materials A and B, whose stress-strain graphs are shown in the figure. The rods are subjected to axial tensile force. Then select the correct option.

Moderate

A

For same tensile force, elongation produced in rod A is more than that of rod B.
B

If the force applied on rod A is less than the force applied on B, then elongation produced in B is more
C

If same elastic potential energy is stored in both rods, then force applied on A is more than the force applied on B
D

Both (2) and (3) are right

Solution

From the stress-strain graph it is evident that $Y_{A} > Y_{B}$
In option - (2), $σ_{A} < σ_{B}$
Since $\in = \frac{σ}{Y}$ it is evident that $\in_{A} < \in_{B}$ . Hence option - (2) is right.
Again energy density, $u = \frac{σ^{2}}{2 Y} = \frac{F^{2}}{2 {YA}^{2}}$
Since $u_{a} = u_{B}$ we can write $\frac{F_{A}^{2}}{Y_{A}} = \frac{F_{B}^{2}}{Y_{B}}$
$\Rightarrow F_{A} = \sqrt{\frac{Y_{A}}{Y_{B}}} F_{B} \Rightarrow F_{A} > F_{B}$
Hence option - (3) is also right.

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