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:
1. $\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\Big(\frac{\Delta T}{T}\Big)$
2. $\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}-2\frac{\Delta T}{T}\Big]$
3. $\frac{\Delta g}{g}=4\pi^2\Big[\frac{\Delta L}{L}+2\frac{\Delta T}{T}\Big]$
4. $\frac{\Delta g}{g}=\frac{\Delta L}{L}-2\Big(\frac{\Delta T}{T}\Big)$

When the circular scale of a screw gauge completes $2$ rotations, it covers $1$ mm over the pitch scale. The total number of circular scale divisions is $50.$ The least count of the screw gauge in metres is:
1. $10^{-4}$
2. $10^{-5}$
3. $10^{-2}$
4. $10^{-3}$