Masses of three wires of copper are in the ratio of 1 : 3 : 5 and their lengths are in the ratio of 5 : 3 : 1. The ratio of their electrical resistance are:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 125 : 15 : 1
Resistance (R) of a wire is
$R=ρ\frac{L}{A}=ρ\frac{L^2}{V}$ $A=\frac{V}{L}$
$R=\frac{ρdL^2}{M}$ [D = Density, $d =\frac{mass}{volume}$]
and, density of all the copper is same.
$∴R_1:R_2:R_3=\frac{5^2}{1}:\frac{3^2}{3}:\frac{1^2}{5}$
$=125:15:1$