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PhysicsElasticityMiscellaneousEasy2 minPYQ_2020

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A rubber cord of density $d,$ Young's modulus $Y$ and length $L$ is suspended vertically. If the cord extends by a length $0.5 L$ under its own weight, then $L$ is

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Answer:

Solution:

$∵$ Young's modulus $Y = \frac{S t r e s s}{S t r a i n}$

$Y = \frac{(\frac{F}{A})}{(\frac{∆ L}{L})}$

$\Rightarrow ∆ l = \frac{F L}{A Y}$

extennsion in $d x$ at $‘ x ’$

$d e = \frac{x d A g (d x)}{A Y}$

total extension $e = \int_{0}^{L} \frac{x d A g (d x)}{A Y}$

$= \frac{d g}{Y} \frac{L^{2}}{2}$

$0.5 L = \frac{d g L^{2}}{Y 2} \Rightarrow L = \frac{Y}{d g}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:ElasticitySubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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