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The density of a solid ball is to be det...

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

A

`0.9%`

B

`2.4%`

C

`3.1%`

D

`4.2%`

Text Solution

Verified by Experts

The correct Answer is:
C
Pitch =0.5mm
L.C. = `("0.5 mm")/50 == 0.01` mm
Diameter = Division on circular scale `xx` Least count + Main scale reading
`= (20 xx0.01)+2.5 = 2.7` mm
`implies D= 2.7` mm
density `(rho)= M/("Volume") =M/(4/3pi(D/2)^3)`
`((Deltap)/rho)xx100=((DeltaM)/M+3(DeltaD)/(D)) xx100`
`= 2 + 3 xx(0.01)/(2.7) xx100 = 2+1.11 =3.1 %`
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