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Physics - Elasticity Question with Solution | TestHub

PhysicsElasticityMiscellaneousMedium2 minPYQ_2021

PhysicsMediumsingle choice

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:

Options:

Answer:

Solution:

In series combination, $Δ l = ℓ_{1} + ℓ_{2}$

$Y = \frac{F / A}{Δ ℓ / ℓ} \Rightarrow Δ ℓ = \frac{F ℓ}{A Y}$

$\Rightarrow Δ ℓ \propto \frac{ℓ}{Y}$

Equivalent length of rod after joining is $= 2 ℓ$

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

$Δ ℓ = Δ ℓ_{1} + Δ ℓ_{2}$

$\frac{ℓ_{eq}}{Y_{eq}} = \frac{ℓ}{Y_{1}} + \frac{ℓ}{Y_{2}} \Rightarrow \frac{2 ℓ}{Y} = \frac{ℓ}{Y_{1}} + \frac{ℓ}{Y_{2}}$

$∴ Y = \frac{2 Y_{1} Y_{2}}{Y_{1} + Y_{2}}$

Stream:JEESubject:PhysicsTopic:ElasticitySubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2021

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