Two wires are made up of same material. Ratio of their masses is 1 : 2 and ratio of their lengths is 2 : 1 . So ratio of their resistances is.... .

Options

A. `1: 4`
B. `4 : 1`
C. `1: 8 `
D. `8: 1 `

Answer

D

Explanation

`8 : 1 `
`R = (rho l)/(A) rArr R = (rho l^(2))/(V) " " [ because Al = V] `
`R = (rho l^(2))/((m)/(d)) ( because " volume " = ("mass")/("density"))`
Material is same, so `rho` and d are constant.
`therefore R prop (l^(2))/(m)`
`therefore (R_(1))/(R_(2)) = ((l_(1))/(l_(2)))^(2) xx ((m_(2))/(m_(1))) `
= ` (2)^(2) xx (2)`
`= 4 xx 2 = 8 `
`therefore R_(1) : R_(2) = 8 : 1 `