First slide

Elastic Modulie

Question

A steel rod is pulled by a force which increases gradually from zero to F and elongation produced in the rod is found to be x. If the some rod is pulled by a constant force 4F, the elongation produced in the rod will be

Moderate

A

6x
B

4x
C

8x
D

2x

Solution

Initially $x = \frac{Fl}{AY}$
In the second case,
elastic potential energy stored in the rod = Work done by 4F
$∴ \frac{1}{2} \frac{AY}{l} . y^{2} = 4 F . y \Rightarrow y = \frac{8 Fl}{AY} = 8 x$

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