Consider copper and aluminium wire whose length and resistance are the same. Also, the specific resistance of aluminium is more than copper. Select the correct statement

The correct option is "The information given is incomplete".

Let us analyze the relationships between the mass, length, resistance, specific resistance (resistivity), and density of the two wires to understand why the given information is insufficient to compare their masses.

First, the resistance $R$ of a wire of length $l$, cross-sectional area $A$, and resistivity (specific resistance) $\rho$ is given by the formula:

$R=\rho \frac{l}{A}$

Rearranging this formula for the cross-sectional area $A$, we get:

$A=\rho \frac{l}{R}$

Next, the volume $V$ of the wire is the product of its cross-sectional area and its length:

$V=A\times l=\rho \frac{l^2}{R}$

The mass $m$ of a wire is given by the product of its volume $V$ and its density $d$:

$m=V\times d=\rho \frac{l^2}{R}\times d$

We are given that the length $l$ and resistance $R$ are the same for both copper (Cu) and aluminium (Al) wires. Therefore, the ratio of their masses depends on their specific resistances (resistivities) and their densities:

$\frac{m_{\mathrm{Cu}}}{m_{\mathrm{Al}}}=\frac{{\rho }_{\mathrm{Cu}}}{{\rho }_{\mathrm{Al}}}\times \frac{d_{\mathrm{Cu}}}{d_{\mathrm{Al}}}$

While the problem mentions that the specific resistance of aluminium is greater than that of copper (${\rho }_{\mathrm{Al}}>{\rho }_{\mathrm{Cu}}$), it does not provide any information about the densities ($d$) of copper and aluminium within the context of the question.

Without the density values of both materials, it is mathematically impossible to determine which wire has more mass or if they are equal. Thus, the information provided is incomplete.