Ratio of diameters of two wires of same material is n : 1 . length of wires are 4, m each. On applyi

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8.Mechanical Properties of Solids

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The ratio of diameters of two wires of same material is $n : 1$. The length of wires are $4\, m$ each. On applying the same load, the increase in length of thin wire will be

A

${n^2}$ times

B

$n$ times

C

$2n$ times

D

None of the above

Solution

(a) $l \propto \frac{{FL}}{{{r^2}Y}}$ $⇒$ $l \propto \frac{1}{{{r^2}}}$ ${\rm{( }}F,L\;{\rm{and }}\,\,Y{\rm{ \,\,are \,\,constant)}}$

$\frac{{{l_2}}}{{{l_1}}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2} = {(n)^2} \Rightarrow {l_2} = {n^2}{l_1}$

Standard 11

Physics

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