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A mild steel wire of length 2L is streth...

A mild steel wire of length `2L` is strethched, within its elastic limit horizontally between two pillars(figure). A mass of `m` is suspended form the midpont of the wire. Strain in the wire is

A

`(x^(2))/(2L^(2))`

B

`(x)/(L)`

C

`(x^(2))/(L)`

D

`(x^(2))/(2L)`

Text Solution

Verified by Experts

The correct Answer is:
A

Increase in length, `DeltaL = (PR + RQ) - PQ = 2PR -PQ` `DeltaL = 2 (L^(2) + x^(2))^(1//2) - L = 2l (1+(x^(2))/(L^(2))) - 2L = 2L [1+(1)/(2)(x^(2))/(L^(2))]-2L" "("By binomial therorem")`
`=(x^(2))/(L)`
`therefore "Strain" =(DeltaL)/(2L) =(x^(2))/(2L^(2))`
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