Q 12-03-291JEE MainJEE Main 2017 (9 Apr)Easy
A uniform wire of length $l$ and radius $r$ has a resistance of $100\ \Omega$. It is recast into a wire of radius $\dfrac r2$. The resistance of new wire will be:
Answer: (A) $1600\ \Omega$
The volume is unchanged, so halving the radius makes the area $\frac14$ and the length $4$ times:
$$R' = \rho\frac{4l}{A/4} = 16R = 1600\ \Omega$$
Solution by Sreeraj P, M.Sc Physics