The length of a wire is increased by $1 m m$ on the application of a given load. In a wire of the same material, but of length and radius twice that of the first, on application of the same load, extension is

0.25 m m

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0.5 m m

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2 m m

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4 m m

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Solution

The correct option is C $0.5 m m$
Young's Modulus of elasticity =stress/strain
$Y = \frac{F / a}{△ l / l}$ or $Y = \frac{F l}{a △ l}$
or $△ l = \frac{F l}{a Y} = \frac{F l}{π r^{2} Y}$
In the given problem, $△ l \propto \frac{l}{r^{2}}$
When both $l$ and $r$ are doubled, $△ l$ is halved.

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The length of a wire is increased by 1 mm on the application of a given load. In a wire of the same material, but of length and radius twice that of the first, on application of the same load, extension is

The correct option is C 0.5 mmYoung's Modulus of elasticity =stress/strainY=F/a△l/l or Y=Fla△lor △l=FlaY=Flπr2YIn the given problem, △l∝lr2When both l and r are doubled, △l is halved.

The length of a wire is increased by $1 m m$ on the application of a given load. In a wire of the same material, but of length and radius twice that of the first, on application of the same load, extension is

The correct option is C $0.5 m m$
Young's Modulus of elasticity =stress/strain
$Y = \frac{F / a}{△ l / l}$ or $Y = \frac{F l}{a △ l}$
or $△ l = \frac{F l}{a Y} = \frac{F l}{π r^{2} Y}$
In the given problem, $△ l \propto \frac{l}{r^{2}}$
When both $l$ and $r$ are doubled, $△ l$ is halved.