Young’s moduli of two wires A and B are in ratio 7 : 4 . Wire A is 2, m long and has radius R

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8.Mechanical Properties of Solids

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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 $A$ is $2\, m$ long and has radius $R$. Wire $B$ is $1.5\, m$ long and has radius $2\, mm$. If the two wires stretch by the same length for a given load, then the value of $R$ is close to ......... $mm$

A

$1.3$

B

$1.5$

C

$1.7$

D

$1.9$

(JEE MAIN-2019)

Solution

Given:

$\frac{{{Y_A}}}{{{Y_B}}} = \frac{7}{4}\,\,\,{L_A} = 2m\,\,\,{A_A} = \pi {R^2}$

${L_B} = 1.5\,m\,\,\,\,\,\,\,\,{A_B} = \pi {\left( {2mm} \right)^2}$

$\frac{F}{A} = Y\left( {\frac{\ell }{L}} \right)$

$given\,F\,and\,\ell \,are\,same \Rightarrow \frac{{AY}}{L}\,is\,same$

$\frac{{{A_A}{Y_A}}}{{{L_A}}} = \frac{{{A_B}{Y_B}}}{{{L_B}}}$

$ \Rightarrow \frac{{\left( {\pi {R^2}} \right)\left( {\frac{7}{4}{Y_B}} \right)}}{2} = \frac{{\pi {{\left( {2\,mm} \right)}^2}.{Y_B}}}{{1.5}}$

$R = 1.74\,mm$

Standard 11

Physics

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