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Physics-

General

Easy

Question

Four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows

L = 100 cm, r = 1mm
L = 200 cm, r = 3mm
L = 300 cm, r = 3mm
L = 400 cm, r = 4mm

The correct answer is: L = 100 cm, r = 1mm

$increment L equals fraction numerator F L over denominator A Y end fraction$
Because, wires of the same material are stretched by the same load. So, F and Y will be constant.
$therefore blank increment L proportional to fraction numerator L over denominator pi r to the power of 2 end exponent end fraction$
$increment L subscript 1 end subscript equals fraction numerator 100 over denominator pi cross times left parenthesis 1 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator 100 over denominator pi cross times 10 to the power of negative 6 end exponent end fraction$
$equals fraction numerator 100 over denominator pi end fraction cross times 10 to the power of negative 6 end exponent$
$therefore increment L subscript 2 end subscript equals fraction numerator 200 over denominator pi cross times left parenthesis 3 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator 200 over denominator pi cross times 9 cross times 10 to the power of negative 6 end exponent end fraction$
$equals fraction numerator 22.2 over denominator pi end fraction cross times 10 to the power of 6 end exponent$
$therefore increment L subscript 3 end subscript equals fraction numerator 300 over denominator pi cross times left parenthesis 3 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator 100 over denominator pi cross times 9 cross times 10 to the power of negative 6 end exponent end fraction$
$equals fraction numerator 33.3 over denominator pi end fraction cross times 10 to the power of 6 end exponent$
$therefore increment L subscript 4 end subscript equals fraction numerator 400 over denominator pi cross times left parenthesis 4 cross times 10 to the power of negative 3 end exponent right parenthesis to the power of 2 end exponent end fraction equals fraction numerator 400 over denominator pi cross times 16 cross times 10 to the power of negative 6 end exponent end fraction$
$equals fraction numerator 25 over denominator pi end fraction cross times 10 to the power of 6 end exponent$
We can see that, L=100 cm and r = 1mm will elongate most.

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