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JEE Main 20209 JanuaryEvening Shift

Exam: JEE Main
Year: 2020
Date: 9 January
Shift: Evening Shift
Subject: Physics
Chapter: Mechanical Properties of Solids

JEE Main 2020 · 9 January · Evening Shift · Physics · Mechanical Properties of Solids

Two steel wires having same length are suspended from a ceiling...

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:

Options

A $\sqrt{2}: 1$
B $1: 2$
C $2: 1$
D $1: \sqrt{2}$

Correct answer

A. $\sqrt{2}: 1$

Step-by-step solution

\dfrac{du}{dv} = \dfrac{1}{2}

stress

\times \dfrac{stress}{y}

= \dfrac{1}{2}\dfrac{{F}^{2}}{{A}^{2}y}

\dfrac{du}{dv}\alpha\dfrac{1}{{d}^{4}}

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

\dfrac{{d}_{1}}{{d}_{2}} = {\left(4\right)}^{1 / 4}

\dfrac{{d}_{1}}{{d}_{2}} = \sqrt{2}: 1

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