Question

An aluminum rod and a copper rod are taken such that their lengths and resistance are same .The specific resistance of copper is half that of aluminum but its density is three times that of aluminum. The ratio of the mass of aluminum 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 $\frac{2}{3}$

$l_a=l_c$, $R_a=R_c$, $d_c=3d_a$, ${\rho }_c=\frac{1}{2}{\rho }_a$
$R=\frac{\rho l}{A}=\frac{\rho l^2}{V}=\frac{\rho l^{2}d}{m}\Rightarrow m=\frac{\rho l^{2}d}{R}$
$\therefore \frac{m_a}{m_c}=\frac{2}{3}$