A slightly conical wire of length L and end radii r1 and r2 is stretched by two forces F, F applied parallel to length in opposite directions and normal to end faces. If Y denotes the Young’s modulus, then extension produced is

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Stress Strain and Hookes Law New

Question

A slightly conical wire of length L and end radii r₁ and r₂ is stretched by two forces F, F applied parallel to length in opposite directions and normal to end faces. If Y denotes the Young’s modulus, then extension produced is

$\frac{FLY}{π r_{1} r_{2}}$

$\frac{FL}{π r_{1} Y}$

$\frac{FL}{π r_{1}^{2} Y}$

$\frac{FL}{π r_{1} r_{2} Y}$

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4L = $\frac{FL}{YA}$
F = YA $\frac{4 ℓ}{L}$

Only option dimensionally correct.