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Two wires have diameters in the ratio 2:...

Two wires have diameters in the ratio `2:1`, lengths in the ratio `4:3` and Young's modulus in the ratio `5:3`. The ratio of elongations produced in the wires when subjected to the same stretching force is

A

`1.5`

B

3

C

`4.5`

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
`Y = (FL)/(pi r^(2) e) :. e = (FL)/(pi r^(2) Y)` but `F_(1) = F_(2)`
`:. (e_(1))/(e_(2)) = ((L_(1))/(L_(2))) ((r_(2))/(r_(1)))^(2)((Y_(2))/(Y_(1)))`
`(3)/(4) xx ((2)/(1))^(2) xx ((3)/(2)) = (9)/(2) = 4.5`
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