Mechanical Properties of Solids

JEE Main level, single correct, medium

114 of 118

Question 114 of 118

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 1:4,1:4, the ratio of their diameters is:

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Answer: (A) 2:1\sqrt{2}:1

dudv=12\dfrac{du}{dv}=\dfrac{1}{2} stress ×stressy\times \dfrac{stress}{y}
=12F2A2y=\dfrac{1}{2}\dfrac{{F}^{2}}{{A}^{2}y}
dudvα1d4\dfrac{du}{dv}\alpha \dfrac{1}{{d}^{4}}
(dudv)1(dudv)2=d24d14=14\dfrac{{\left(\dfrac{du}{dv}\right)}_{1}}{{\left(\dfrac{du}{dv}\right)}_{2}}=\dfrac{{d}_{2}^{4}}{{d}_{1}^{4}}=\dfrac{1}{4}
d1d2=(4)1/4\dfrac{{d}_{1}}{{d}_{2}}={\left(4\right)}^{1/4}
d1d2=2:1\dfrac{{d}_{1}}{{d}_{2}}=\sqrt{2}:1

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