The diameter of the solid ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 5

Question

The diameter of the solid ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of $1.5 \%$, the relative percentage error in the density is

Professor PC Thomas Classes · Answer

Radius error contributes 3 times to volume error. Density error $\frac{\Delta \rho}{\rho} = \frac{\Delta m}{m} + 3\frac{\Delta r}{r}$.