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. (a) `0.9%`
B. (b) `2.4%`
C. ( c ) `3.1%`
D. (d) `4.2%`

Answer

C

Explanation

( c ) Diameter `D = M.S.R. + (C.S.R)xxL.C.`
`D = 2.5 + 20 xx(0.5)/(50)`
`D = 2.70mm`
The uncertainty in the measurement of diameter
`DeltaD = 0.01mm`.
we know that `rho =(Mass)/(Volume) = (M)/(V) = (M)/((4)/(3)pi((D)/(2))^(3)`
:. `(Deltarho)/(rho)xx100 = (DeltaM)/(M) xx100 + 3(DeltaD)/(Delta)xx100`
`=2+3xx(0.01)/(2.70)xx100 = 3.1%`