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Physics-

General

Easy

Question

Two bars $A$ and $B$ of circular cross section, same volume and made of the same material, are subjected to tension. If the diameter of $A$ is half that of $B$ and if the force applied to both the rod is the same and it is in the elastic limit, the ratio of extension of $A$ to that of $B$ will be

16
8
4
2

The correct answer is: 16

$Y equals fraction numerator F l over denominator a to the power of 2 end exponent increment l blank end fraction$
$increment l proportional to fraction numerator 1 over denominator a to the power of 2 end exponent end fraction o r blank increment l proportional to fraction numerator 1 over denominator D to the power of 4 end exponent end fraction$
$fraction numerator increment l subscript A end subscript over denominator increment l subscript B end subscript end fraction equals fraction numerator D subscript B end subscript superscript 4 end superscript over denominator D subscript A end subscript superscript 4 end superscript end fraction equals fraction numerator 1 to the power of 4 end exponent over denominator open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 4 end exponent end fraction equals 16$
$Y equals fraction numerator F over denominator a end fraction cross times fraction numerator l over denominator increment l end fraction$
Now, $V equals a l$ or $l equals fraction numerator Y over denominator a end fraction blank therefore Y equals fraction numerator F V over denominator a to the power of 2 end exponent increment l end fraction$

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