The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is `0.5mm` and there are `50` divisions on the circular scale. The reading on the main scale is `2.5mm` and that on circular scale is `20` divisions. if the measured mass of the ball has a relative error of `2%`, the relative percentage error in the density is

Options

A. `0.9%`
B. `2.4%`
C. `3.1%`
D. `4.2%`

Answer

C

Explanation

Least count of screw gauge `=(0.5)/(50)=0.01mm`
`diameter=2.5+20(0.01)=2.7mm`
`Relative error in density (Deltarho)/(rho)=(DeltaM)/(M)+3[(DeltaD)/(D)]`
relative error
`(Deltarho)/(rho)xx100=2%+3[(0.01)/(2.7)]100=3.11%`