QJEEM24Ph9db7: JEE Main 2024 Physics - Class 11 JEEM24Ph9db7 Solution: A wire of length L and radius r is clamped at one end. If its…

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QJEEM24Ph9db7: JEE Main 2024 Physics - Class 11 JEEM24Ph9db7 Solution: A wire of length L and radius r is clamped at one end. If its…

A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$ , its length increases by $l$ . If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Multiple Choice Options

A 2 times
B 4 times
C 3 times
D 32 times

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Accepted Answer

$\begin{aligned} Y = \frac{stress}{strain} \\ Y = \frac{\frac{F}{\frac{π r^{2}}{ℓ}}}{\frac{ℓ}{L}} \end{aligned}$

$F = Y π r^{2} \times \frac{ℓ}{L} .... (i)$

$\begin{aligned} Y = \frac{\frac{F / 2}{π r^{2} / 4}}{\frac{Δ ℓ}{L}} \\ F = Y \frac{Δ ℓ}{L} \times 2 \times \frac{π r^{2}}{4} \end{aligned}$

From (i)

$\begin{aligned} Y π r^{2} \frac{ℓ}{L} = Y \frac{Δ ℓ}{L} \frac{π r^{2}}{2} \\ Δ ℓ = 2 ℓ \end{aligned}$

QJEEM24Ph9db7: JEE Main 2024 Physics - Class 11 JEEM24Ph9db7 Solution: A wire of length L and radius r is clamped at one end. If its…

Multiple Choice Options

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