Two wires of same length and radius are joined… - JEE Main 2021 Physics PYQ

JEE Main 2021 — Physics Mechanics

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Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are ${Y}_{1}$ and ${Y}_{2}$ . The combination behaves as a single wire then its Young's modulus is:

Official previous-year question

Held on 25 Jul 2021 · Verified 6 Jul 2026.

Options

A
$Y=\frac{2{Y}_{1}{Y}_{2}}{3({Y}_{1}+{Y}_{2})}$
B
$Y=\frac{2{Y}_{1}{Y}_{2}}{{Y}_{1}+{Y}_{2}}$
C
$Y=\frac{{Y}_{1}{Y}_{2}}{2({Y}_{1}+{Y}_{2})}$
D
$Y=\frac{{Y}_{1}{Y}_{2}}{{Y}_{1}+{Y}_{2}}$

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Solution

In series combination, $\Delta l={\ell }_{1}+{\ell }_{2}$

$Y=\frac{F/A}{\Delta \ell /\ell }\Rightarrow \Delta \ell =\frac{F\ell }{AY}$

$\Rightarrow \Delta \ell \propto \frac{\ell }{Y}$

Equivalent length of rod after joining is $=2\ell$

As, lengths are same and force is also same in series

$\Delta \ell =\Delta {\ell }_{1}+\Delta {\ell }_{2}$

$\frac{{\ell }_{\mathrm{eq}}}{{Y}_{\mathrm{eq}}}=\frac{\ell }{{Y}_{1}}+\frac{\ell }{{Y}_{2}}\Rightarrow \frac{2\ell }{Y}=\frac{\ell }{{Y}_{1}}+\frac{\ell }{{Y}_{2}}$

$\therefore Y=\frac{2{Y}_{1}{Y}_{2}}{{Y}_{1}+{Y}_{2}}$

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Options

$Y=\frac{2{Y}_{1}{Y}_{2}}{3({Y}_{1}+{Y}_{2})}$

$Y=\frac{2{Y}_{1}{Y}_{2}}{{Y}_{1}+{Y}_{2}}$

$Y=\frac{{Y}_{1}{Y}_{2}}{2({Y}_{1}+{Y}_{2})}$

$Y=\frac{{Y}_{1}{Y}_{2}}{{Y}_{1}+{Y}_{2}}$

Solution

In series combination, $\Delta l={\ell }_{1}+{\ell }_{2}$

$Y=\frac{F/A}{\Delta \ell /\ell }\Rightarrow \Delta \ell =\frac{F\ell }{AY}$

$\Rightarrow \Delta \ell \propto \frac{\ell }{Y}$

Equivalent length of rod after joining is $=2\ell$

As, lengths are same and force is also same in series

$\Delta \ell =\Delta {\ell }_{1}+\Delta {\ell }_{2}$

$\frac{{\ell }_{\mathrm{eq}}}{{Y}_{\mathrm{eq}}}=\frac{\ell }{{Y}_{1}}+\frac{\ell }{{Y}_{2}}\Rightarrow \frac{2\ell }{Y}=\frac{\ell }{{Y}_{1}}+\frac{\ell }{{Y}_{2}}$

$\therefore Y=\frac{2{Y}_{1}{Y}_{2}}{{Y}_{1}+{Y}_{2}}$

Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

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Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics