A wire of length 10 cm and radius $\sqrt{7}\times {10}^{-4}$ m connected across the right gap of a meter bridge. When a resistance of $4.5\Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at 60 cm from the left end. If the resistivity of the wire is $R\times {10}^{-7}\Omega m,$ then value of R is       [2024]

Wheatstone bridge principle is used to measure the specific resistance $\left(S_1\right)$ of given wire, having length L, radius r. If X is the resistance of wire, then specific resistance is; $S_1=X\left(\frac{\pi r^2}{L}\right)$.

If the length of the wire gets doubled then the value of specific resistance will be:                  [2024]