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A wire of length L and radius r is fixed...

A wire of length `L` and radius `r` is fixed at one end. When a stretching force `F` is applied at free end, the elongation in the wire is `l`. When another wire of same material but of length `2L` and radius `2r`, also fixed at one end is stretched by a force `2F` applied at free end, then elongation in the second wire will be

A

1

B

2 1

C

`1/2`

D

4 1

Text Solution

Verified by Experts

The correct Answer is:
A
`F=kX,(F_(1))/(F_(2))=(k_(1)X_(1))/(k_(2)X_(2))or,(X_(2))/(X_(1))=(k_(1)F_(2))/(k_(2)F_(1))or,(X_(2))/(X_(1))=(A_(1)F_(2)l_(2))/(l_(1)A_(2)F_(1))=(A*2F*2l)/(4A*l*F)=1`
`X_(2)=X_(1)=l`
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