Two wire of the same material and length stretched by the same force. If the ratio of the radii of the two wires is n : 1 then the ratio of their elongations is

Options

A. `n^(2) : 1`
B. `1 : n^(2)`
C. `1 : n`
D. `n : 1`

Answer

B

Explanation

The two wires have the same length, same material and stretched by the same force (Mg) and `(r_(1))/(r_(2)) = n : 1`.
`because Y = (M g L)/(pi r^(2) e) :. E = (M gL)/(pi r^(2) Y) :. e prop (1)/(r^(2))`
`:. (e_(1))/(e_(2)) = (r_(2)^(2))/(r_(1)^(2)) = ((1)/(n))^(2) :. (e_(1))/(e_(2)) = 1 : n^(2)`