Two wires A and B are of same material. Their lengths are in the ratio 1:2 and diameters are in the ratio 2:1. When stretched by forces `F_(A)andF_(B)` respectively, they get equal increase in their lengths. Then the ratio `F_(A)//F_(B)` should be:

Options

A. `1:1`
B. `1:2`
C. `8:1`
D. `2:1`

Answer

C

Explanation

As both wires of same material
`Y_(A)=Y_(B)`
`(F_A)/(pi(r_A)^(2)).(l_A)/(Deltal_A)=(F_B)/(pi(r_B)^(2)).(l_B)/(Deltal_B)`
But, `Deltal_(A)=Deltal_(B)`
`rArr(F_A)/(F_B)=(I_B)/(I_A).((r_A)/(r_B))^(2)=(2)/(1)((2)/(1))^(2)`
`=8:1`