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%`

Explanation

Least count `= (0.5)/(50) = 0.01 mm`
Diameter of ball `D = 2.5 mm + (20) (0.01)`
`D = 2.7 mm`
`rho = (M)/(vol) = (M)/(4/(3)pi((D)/(2))^(3))`
`((Deltarho)/(rho))_(max)=(Deltam)/(m)+3(DeltaD)/(D)((Deltarho)/(rho))_(max)=2%+3((0.01)/(2.7))xx100%`
`(Deltarho)/(rho) = 3.1%` .