Masses of 3 wires of same metal are in the ratio `1 : 2 : 3` and their lengths are in the ratio `3 : 2 : 1`. The electrical resistances are in ratio

Options

A. `1 : 4 : 9`
B. `9 : 4 : 1`
C. `1 : 2 : 3`
D. `27 : 6 : 1`

Answer

D

Explanation

(d) `R prop (l^(2))/(m) implies R_(1) : R_(2) : R_(3) = (l_(1)^(2))/(m_(1)) : (l_(2)^(2))/(m_(2)) : (l_(3)^(2))/(m_(3))`
`implies R_(1) : R_(2) : R_(3) = (9)/(1) : (4)/(2) : (1)/(3) = 27 : 6 : 1`