Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is:
Solution
${{du} \over {dv}}$ = ${1 \over 2}$ $\times$ stress × strain
<br><br>= ${1 \over 2}{F \over A} \times {F \over {AY}}$ $\propto$ ${1 \over {{A^2}}}$ $\propto$ ${1 \over {{d^4}}}$
<br><br>${{du} \over {dv}}$ = ${1 \over 4}$
<br><br>$\Rightarrow$ ${\left( {{{{d_1}} \over {{d_2}}}} \right)^4}$ = 4
<br><br>$\Rightarrow$ ${{{d_1}} \over {{d_2}}} = {\left( 4 \right)^{{1 \over 4}}}$ = $\sqrt 2 :1$
About this question
Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity
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