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) (0.01) = 2.7 mm`
`rho = (M)/( Vol) = (M)/((4)/( 3) pi (( D)/(2))^(3))`
`(( Delta rho)/( rho)) = ( Delta m)/( m) + 3 ( Delta D)/( D) = 2% + 3((0.01)/( 2.7)) xx 100% = 3.1%`