The ratio of length of two wires of same mass arc made up of same material is 1 : 2 Therefore ratio of their resistance is ........

Options

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

Answer

D

Explanation

`1: 4`
`R = (rho l)/(A) = (rho l^(2))/(V) = (rho l^(2) d)/(m)`
` " (Density" d = (m)/(V) rArr V = (m)/(d) `
`R prop l^(2) ` (other terms are equal.
`therefore (R_(1))/(R_(2)) = ((l_(1))/(l_(2)))^(2) = ((1)/(2))^(2) = (1)/(4) `