Two steel wires having the 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 :

Answers (1)

\frac{du}{dv}=\frac{1}{2}stress\times \frac{stress}{Y }

=\frac{1}{2}\frac{F^{2}}{A^{2}Y }

\frac{du}{dv}\propto \frac{1}{d^{4}}

\frac{\left ( \frac{du}{dv} \right )_{1}}{(\frac{du}{dv} )_{2}}=\frac{d^{4}_{2}}{d^{4}_{1}}=\frac{1}{4}

    \frac{d_{1}}{d_{2}}=(4)^{1/4}

    \frac{d_{1}}{d_{2}}=\sqrt{2}:1

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