Question

Two wires made of same material have their electrical resistances in the ratio 1 : 4. If their lengths are in the ratio 1 : 2, the ratio of their masses is:

• A. 1: 1
• B. 1 : 8
• C. 8 : 1
• D. 2 : 1

Answer 1

The correct option is A 1: 1

$\frac{R_1}{R_2}=\frac{1}{4}$

$\frac{\frac{\rho L_1}{A_1}}{\frac{\rho L_2}{A_2}}=\frac{1}{4}$

$\Rightarrow \frac{L_1}{L_2}\left(\frac{A_2}{A_1}\right)=\frac{1}{4}$

$\frac{1}{2}\left(\frac{A_2}{A_1}\right)=\frac{1}{4}$

$\frac{A_1}{A_2}=\frac{2}{1}$

$\Rightarrow \frac{m_1}{m_2}=\frac{L_1{A}_1}{L_2{A}_2}$

$=\left(\frac{L_1}{L_2}\right)\left(\frac{A_1}{A_2}\right)$

$=\frac{1}{2}\times \frac{2}{1}=1$

$m_1=m_2$