Q 12-03-080JEE MainJEE Main 2024 (4 Apr, Shift 2)Medium
Two wires A and B are made of the same material and have the same mass. Wire A has a radius of $2.0\ \text{mm}$ and wire B has a radius of $4.0\ \text{mm}$. The resistance of wire B is $2\ \Omega$. The resistance of wire A is ______ $\Omega$.
Numerical value type. Enter your answer.
Answer: 32
Same mass and material means the same volume, so $l \propto \dfrac{1}{r^2}$. Then
$$R = \frac{\rho l}{\pi r^2} \propto \frac{1}{r^4}$$
$$R_A = R_B\left(\frac{r_B}{r_A}\right)^4 = 2\times2^4 = 32\ \Omega$$
Solution by Sreeraj P, M.Sc Physics