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Physics - Elasticity Question with Solution | TestHub

PhysicsElasticityMiscellaneousHard2 minPYQ_2021

PhysicsHardnumerical

A uniform metallic wire is elongated by $0.04 m$ when subjected to a linear force $F .$ The elongation, if its length and diameter is doubled and subjected to the same force will be _________ $cm .$

Answer:

2.00

Solution:

$F = Y . A \cdot \frac{Δ l}{l}$ $\Rightarrow Δ l = \frac{F}{Y . A .} \cdot l$ $\Rightarrow Δ l = \frac{F . l}{Y . π r^{2}}$ $\Rightarrow Δ l \propto \frac{l}{r^{2}}$

$\frac{Δ l_{2}}{Δ l_{1}} = (\frac{l_{2}}{l_{1}}) {(\frac{r_{1}}{r_{2}})}^{2}$ $= (2) {(\frac{1}{2})}^{2}$ $\Rightarrow \frac{Δ l_{2}}{Δ l_{1}} = \frac{1}{2}$ $\Rightarrow Δ l_{2} = \frac{Δ l_{1}}{2}$

$= \frac{0.04}{2}$ $= 0.02 m$ $\Rightarrow Δ l_{2} = 2 cm$ .

Stream:JEESubject:PhysicsTopic:ElasticitySubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2021

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