In an experiment to determine the specific resistance ( ) of a...

The formula for specific resistance is $\rho = \dfrac{R \pi d^2}{4l}$.

The maximum percentage error in $\rho$ is given by the sum of the percentage errors of the individual quantities, taking into account their powers. Errors always add up to give the maximum possible error, regardless of whether the quantity is in the numerator or denominator:

$\dfrac{\Delta \rho}{\rho} \times 100 = \dfrac{\Delta R}{R} \times 100 + 2 \left( \dfrac{\Delta d}{d} \times 100 \right) + \dfrac{\Delta l}{l} \times 100$

Given that the maximum percentage error in $\rho$ is $8\%$, in $R$ is $2\%$, and in $l$ is $1\%$, we can substitute these values into the equation:

$8\% = 2\% + 2 \times (\text{percentage error in } d) + 1\%$

$8\% = 3\% + 2 \times (\text{percentage error in } d)$

$2 \times (\text{percentage error in } d) = 5\%$

$\text{Percentage error in } d = 2.5\%$

Answer: $2.5\%$