Question

An aluminium rod and a copper rod are taken such that their lengths are same and their resistances are also same. The specific, resistance of copper is half that of aluminium, but its density is three times that of aluminium. The ratio of the mass of aluminium rod and that of copper rod will be

• A. $ \frac{1}{6} $
• B. $ \frac{2}{3} $
• C. $ \frac{1}{3} $
• D. $ 6 $

Answer 1

The Correct Option is B

Resistance of wire is given by $R=\rho \cdot \frac{l}{A} \ldots$ (i)
where $p$ is specific resistance of wire,
$A$ is area of cross-section of wire,
and $l$ is length of wire.
If $V$ is volume of wire, then
$R=\rho \cdot \frac{l^{2}}{V} \ldots$ (ii)
If $d$ is density and $m$ is mass of wire,
then $R=\rho \cdot \frac{l^{2} d}{m}$
$\therefore m \propto \rho d$
$\therefore \frac{m_{A l}}{m_{C u}}=\frac{\rho_{A l}}{\rho_{C u}} \times \frac{d_{A l}}{d_{C u}}$
$=\frac{2}{1} \times \frac{1}{3}=\frac{2}{3}$