Question

The electrical resistance of a mercury column in a cylindrical container is ‘R’. The mercury is poured into another cylindrical container with half the radius of cross-section. The resistance of the mercury column is

• A. R
• B. 2R
• C. 16R
• D. 5R

Answer 1

The correct option is C 16R

$V_1=V_{2}R=\frac{\rho L_1}{A_1}$

$L_1{A}_1=L_2{A}_2$

$L_1\pi r^2=L_2\frac{\pi r^2}{4}\frac{A_1}{A_2}=\frac{4}{1}$

$L_1{L}_2=\frac{1}{4}$

$R^{\prime }=\frac{\rho L_2}{A_2}$

$=\frac{\rho \times 4L_1}{\frac{A_1}{4}}$

$R^{\prime }=16\frac{\rho L_1}{A_1}$

$R^{\prime }=16R$