Two wires made of the same material have lengths 3 m and 4 m and weight 18 gm and 16 gm respectively. When they are subjected to the same tension, ratio of their elongations is

Options

A. `1:2`
B. `2:1`
C. `57:64`
D. `4:1`

Answer

A

Explanation

`(l_(1))/(l_(2))=(L_(1))/(L_(2)) xx (A_(2))/(A_(1)) = (L_(1))/(L_(2))xx(A_(2))/(A_(1))`
`M_(1)=rho v_(1) = rho A_(1)L_(1)`
`M_(2)=rho v_(2) = rho A_(2)L_(2)`
`(M_(1))/(M_(2))=(A_(1))/(A_(2)) xx (L_(1))/(L_(2)) therefore (A_(1))/(A_(2)) =(M_(1))/(M_(2)) xx (L_(2))/(L_(1))`
`therefore (l_(1))/(l_(2)) =(L_(1))/(L_(2))xx(M_(2))/(M_(1)) xx (L_(1))/(L_(2)) = (L_(1)^(2))/(L_(2)^(2)) xx (M_(2))/(M_(1))`
`=(9)/(16)xx (16)/(18) =(1)/(2)`.