The determination of the value of acceleration due to gravity ($g$) by simple pendulum method employs the form

Question

The determination of the value of acceleration due to gravity ($g$) by simple pendulum method employs the formula, $g = 4\pi^2 \frac{L}{T^2}$. The expression for the relative error in the value of $g$ is:

Accepted Answer

Given formula for acceleration due to gravity is:
$$g = 4\pi^2 \frac{L}{T^2}$$
In measuring physical quantities, to find the maximum possible relative error, the relative errors of the individual quantities are added, multiplied by their respective powers. Since $4\pi^2$ is a constant, its error is zero.
The relative error in $g$ is given by:
$$\frac{\Delta g}{g} = \frac{\Delta L}{L} + 2\frac{\Delta T}{T}$$

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