We have two wires $A$ and $B$ of same mass and same material. The diameter of the wire $A$ is half of that $B$. If the resistance of wire $A$ is $24\, ohm$ then the resistance of wire $B$ will be ................ $Ohm$
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(c) Same mass, same material i.e. volume is same or $Al=$ constant
Also, $R = \rho \frac{l}{A}$ $ \Rightarrow $ $\frac{{{R_1}}}{{{R_2}}} = \frac{{{l_1}}}{{{l_2}}} \times \frac{{{A_2}}}{{{A_1}}} = {\left( {\frac{{{A_2}}}{{{A_1}}}} \right)^2}{\left( {\frac{{{d_2}}}{{{d_1}}}} \right)^4}$
$ \Rightarrow $ $\frac{{24}}{{{R_2}}} = {\left( {\frac{d}{{d/2}}} \right)^4} = 16$ $ \Rightarrow $ ${R_2} = 1.5\,\Omega $.
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