question_answer

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 [JEE MAIN Held on 09-01-2020 Evening]

A)  \[\sqrt{2}:1\]    

B)       \[2:1\] C)  \[1:\sqrt{2}\]     D)       \[1:2\] Correct Answer: A Solution : [a] Energy density \[=\frac{1}{2}\,stress\times strain\]

Energy density\[=\frac{1}{2}\frac{F}{A}\times \frac{F}{AY}\]

\[\frac{{{u}_{1}}}{{{u}_{2}}}={{\left( \frac{{{d}_{2}}}{d{{}_{1}}} \right)}^{4}}\]

\[\frac{{{d}_{1}}}{{{d}_{2}}}={{\left( 4 \right)}^{1/4}}\]

\[\frac{{{d}_{1}}}{{{d}_{2}}}=\sqrt{2}:1\]