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

Options

A. `5//9`
B. `4//9`
C. `1//3`
D. `1//5`

Answer

D

Explanation

`(l_(1))/(l_(2))=(L_(1))/(L_(2)) xx (A_(2))/(A_(1))xx(y_(2))/(y_(1))`
`=(4)/(3) xx (r_(2)^(2))/(r_(1)^(2)) xx (3)/(5)=(4)/(5)xx(1)/(4)=(1)/(5)`.