A metal wire has mass \((0.4\pm 0.002)~\text{g}\), radius \((0.3\pm 0.001)~\text{mm}\) and length \((5\pm 0.02)~\text{cm}\). The maximum possible percentage error in the measurement of density will nearly be:
1. \(1.4 \%\)
2. \(1.2 \%\)
3. \(1.3 \%\)
4. \(1.6 \%\)

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. \(10^{-3}\)