A student measures the acceleration due to gravity ( g ) using a...

The formula for acceleration due to gravity using a simple pendulum is $g = \dfrac{4\pi^2 L}{T^2}$.

The fractional error in the time period $T$ is equal to the fractional error in the total time $t$ for $N$ oscillations, i.e., $\dfrac{\Delta T}{T} = \dfrac{\Delta t}{t}$.

The maximum percentage error in $g$ is given by:
$\dfrac{\Delta g}{g} \times 100 = \left(\dfrac{\Delta L}{L} + 2\dfrac{\Delta t}{t}\right) \times 100$

Given values:
$L = 20.0$ cm, $\Delta L = 0.1$ cm
$t = 20.0$ s, $\Delta t = 0.1$ s

Calculating individual percentage errors:
Percentage error in $L = \dfrac{0.1}{20.0} \times 100 = 0.5\%$
Percentage error in $t = \dfrac{0.1}{20.0} \times 100 = 0.5\%$

Maximum percentage error in $g = 0.5\% + 2(0.5\%) = 0.5\% + 1.0\% = 1.5\%$

Answer: $1.5\%$