The radii and Young's moduli of two uniform wires A and B are in the ratio `2:1` and `1:2` respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire A is one percent, the percentage increase in length of the wire B is

Options

A. `1.0`
B. `1.5`
C. `2.0`
D. `3.0`

Answer

C

Explanation

Young's modulus, `Y =(FL)/(pir^(2)DeltaL)`
or `(DeltaL)/(L) =(F)/(pir^(2)Y)`
For the same force,
`therefore ((DeltaL_(B))/(L_(B)))/((DeltaL_(A))/(L_(A))) = ((r_(A))/(r_(B)))^(2) ((Y_(A))/(Y_(B))) = ((2)/(1))^(2) ((1)/(2))=2`
`(DeltaL_(B))/(L_(B)) = 2 ((DeltaL_(A))/L_(A))`
`(DeltaL_(B))/(L_(B))xx 100= 2 ((DeltaL_(A))/(L_(A)) xx 100)=2%`