Question

An aluminium rod and 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

Answer: (B)

Resistance of wire of length land area of cross-section A is
$ R = \rho . \frac {l}{A} \, \, \, \, \, \, \, \, \, \, \, \, \, ....(i)$
If V is volume of wire, then
$ R = \rho . \frac {l^2}{V} \, \, \, \, \, \, \, \, \, \, \, \, \, ....(ii)$
If dis density and mis mass of wire, then
$ \, \, \, \, \, \, \, \, \, R = \rho . \frac {l^2d}{m}$
$\therefore \, \, \, \, \, \, \, m \propto pd $
$\therefore \, \, \, \, \, \, \, \frac {m_{Al}}{m_{Cu}} = \frac {\rho _{Al}}{\rho _{Cu}} \times \frac {d_{Al}}{d_{Cu}}$
$ \, \, \, \, \, \, \, \, = \frac {2}{1}\times \frac {1}{3} = \frac {2}{3}$