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A wire of length L and radius a rigidlyl...

A wire of length L and radius a rigidlyl fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is L, if another wire of same material but of length 2 L and radius 2 a is stretched with a force 2 F, the increase in its length will be

A

l

B

2l

C

`(l)/(2)`

D

`(l)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(Delta l_(1))/(Delta l_(2))= (F_(1 ) l_(1))/(A_(1) Y) xx (A_(2) Y)/(F_(2) l_(2)) = ((F_(1))/(F_(2))) ((l_(1))/(l_(2))) ((r_(2)^(2))/(r_(1)^(2)))`
`rArr (Delta l_(1))/(Delta l_(2))= ((1)/(2)) ((1)/(2)) ((2r)/(r))^(2) = 1 rArr Delta l_(1)= Delta l_(2)= l`
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