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Two wires 'A' and 'B' of the same materi...

Two wires 'A' and 'B' of the same material have radii in the ratio `2:1` and lengths in the ratio `4:1`. The ratio of the normal forces required to produce the same change in the lengths of these two wires is

A

`1 : 2`

B

`1 : 1`

C

`2 : 1`

D

`1 : 4`

Text Solution

Verified by Experts

The correct Answer is:
B
`Y = ((F)/(A))/((Deltal)/(L)) = (FL)/(ADeltal) :. F = YA(DeltaL)/(L) = Y . pir^(2)(DeltaL)/(L)`
The two wires have the same Y and `DeltaL`
`:. F prop (r^(2))/(L)`
`:. (F_(1))/(F_(2)) = ((r_(1))/(r_(2)))^(2) xx ((L_(2))/(L_(1))) = ((2)/(1))^(2) xx ((1)/(4)) = 1`
`:. F_(1) : F_(2) = 1 : 1`
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