In an experiment to determine the acceleration due to gravity ( g )...

The formula for the acceleration due to gravity is:

$g = \dfrac{4\pi^2 L}{T^2}$

The maximum percentage error in $g$ is the sum of the percentage errors in the measured quantities, multiplied by the absolute values of their respective powers. Constants like $4\pi^2$ do not contribute to the error.

$\dfrac{\Delta g}{g} \times 100 = \left(\dfrac{\Delta L}{L} \times 100\right) + 2\left(\dfrac{\Delta T}{T} \times 100\right)$

Given:
Maximum percentage error in $g = 6\%$
Percentage error in $L = 2\%$

Substituting the values:

$6\% = 2\% + 2\left(\dfrac{\Delta T}{T} \times 100\right)$

$2\left(\dfrac{\Delta T}{T} \times 100\right) = 6\% - 2\% = 4\%$

$\dfrac{\Delta T}{T} \times 100 = \dfrac{4\%}{2} = 2\%$

The percentage error in the measurement of time period $T$ is $2\%$.

Answer: $2\%$