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 leangth of the wire A is one percent, the percentage increae 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^2triangleL)`
or `(triangleL)/(L)=(F)/(pir^2Y)`
For the force ,
`((triangleL)/(L_B))/((triangleL_A)/(triangleL_A))=((r_A)/(r_B))^2((Y_A)/(Y_B))=((2)/(1))^2((1)/(2))=2`
`(triangleL_B)/(L_B)=2(triangleL_A)/(L_A)`
`(L_B)/(L_B)xx100=2((triangleL_A)/(L_A)xx100)=2%`