The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

length = 200 cm, diameter = 2 mm

length = 300 cm, diameter = 3 mm

length = 100 cm, diameter = 1 mm

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Properties of Matter question

2013 · Q153

Properties of Matter question

2013 · Q153

View written solutionFree

Correct answer: C

$F = {{YA} \over L} \times \ell$

So, extension, $\ell \propto {L \over A} \propto {L \over {{D^2}}}$
[ $\therefore$ F and Y are constant]

${\ell _1} \propto {{100} \over {{1^2}}} \propto 100$ and ${\ell _2} \propto {{200} \over {{2^2}}} \propto 50$

${\ell _3} \propto {{300} \over {{3^2}}} \propto {{100} \over 3}$ and ${\ell _4} \propto {{50} \over {{1 \over 4}}} \propto 200$

The ratio of ${L \over {{D^2}}}$ is maximum for case (length = 50 cm, diameter = 0.5 mm)

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Properties of Matter question

2013 · Q153

Properties of Matter question

2013 · Q153

View written solutionFree

Correct answer: C

$F = {{YA} \over L} \times \ell$

So, extension, $\ell \propto {L \over A} \propto {L \over {{D^2}}}$
[ $\therefore$ F and Y are constant]

${\ell _1} \propto {{100} \over {{1^2}}} \propto 100$ and ${\ell _2} \propto {{200} \over {{2^2}}} \propto 50$

${\ell _3} \propto {{300} \over {{3^2}}} \propto {{100} \over 3}$ and ${\ell _4} \propto {{50} \over {{1 \over 4}}} \propto 200$

The ratio of ${L \over {{D^2}}}$ is maximum for case (length = 50 cm, diameter = 0.5 mm)