Q85 / 90 · JEE Main 2019 (08 Apr Shift 2) · Physics

Young's moduli of two wires $A$ and $B$ are in the ratio $7 : 4$ . Wire $A$ is $2 m$ long and has radius $R .$ Wire $B$ is $1.5 m$ long and has radius $2 m m .$ If the two wires stretch by the same length for a given load, the value of $R$ is close to:

A
$1.3 m m$
B
$1.9 m m$
C
$1.5 m m$
Correct answer
D
$1.7 m m$

Solution

Strain

= ∆ l / l

Stress

= F / A

Young’s modulus

= \frac{S t r e s s}{S t r a i n} = \frac{F / A}{(∆ l / l)} = \frac{F}{A} (\frac{l}{∆ l})

\frac{Y_{A}}{Y_{B}} = (\frac{l_{A}}{A_{A}}) (\frac{A_{B}}{l_{B}}) = \frac{7}{4}

(\frac{2}{π r_{A}^{2}}) (\frac{π r_{B}^{2}}{1.5}) = \frac{7}{4}

r_{A}^{2} = \frac{2}{1.5 \times 7} \times {(2 m m)}^{2}

r_{A} = 1.7 m m

Hence, the correct answer is option: 'D'.

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