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 `=0.5/50=0.01 mm`
Diameter of ball `D =2.5 mm+(20) (0.001)=2.7 mm`
`rho=M/("Vol")=M/(4/3 pi(D/2)^(3))`
`((Delta rho)/rho)=(Deltam)/m+3(DeltaD)/D=2%+3(0.01/2.7)xx100%=3.1 %`