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A wire of natural length l, Young's modu...

A wire of natural length l, Young's modulus Y and area of cross-section A is extended by x. Then the energy stored in the wire is given by

A

`(1)/(2)(YA)/(l)x^(2)`

B

`(1)/(3)(YA)/(l)x^(2)`

C

`(1)/(2)(Yl)/(A)x^(2)`

D

`(1)/(2)(YA)/(l^(2))x^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Energy stored in the wire
`U=(1)/(2)Yxx("strain")^(2)xx"volume"`
or `U=(1)/(2)Yxx((x)/(l))^(2)xxAl`
or `U=(1)/(2)xx(Yx^(2))/(l)xxA`
or `U=(1)/(2)xx(YA)/(l)x^(2)`
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