Question

Two wires of same material and same length have their resistances in the ratio 5 : 7. The ratio of the masses of the wires is

• A. 5 : 7
• B. 7 : 5
• C. 3 : 4
• D. 4 : 3

Answer 1

The correct option is B 7 : 5

Let resistance of wire 1 be $R_1$

and of wire 2 be $R_2$

$R_1=\frac{{\rho }_1{L}_1}{A_1}{R}_2=\frac{{\rho }_2{L}_2}{A_2}$

Given wires are of same material and same length.

$\Rightarrow {\rho }_1={\rho }_2:L_1=L_2$

$\Rightarrow R_1=\frac{\rho L}{A_1}{R}_2=\frac{\rho L}{A_2}$

$\frac{R_1}{R_2}=\frac{A_2}{A_1}\Rightarrow \frac{A_1}{A_2}=\frac{7}{5}$

Let the mass of wire a be $M_1$ and

of wire 2 be $M_2$

$M_1=\rho V_1{M}_2=\rho V_2$

$\frac{M_1}{M_2}=\frac{\rho L{A}_1}{\rho L{A}_2}$

$\frac{M_1}{M_2}=\frac{A_1}{A_2}=\frac{7}{5}$