The measure of mass and volume of a body are 2.00 g and `5.0 cm^3` respectively, with possible errors of 0.01g and `0.1 cm^3`. What would be the maximum permissible error in its density?

Options

A. `2.54%`
B. `4.2%`
C. `6.4%`
D. `9.2%`

Answer

A

Explanation

Density, `d=("Mass(m)")/("Volume (V)")`
Here `m=2.42g, Deltam =0.01 g. V=4.7cm^(3), DeltaV=0.1" cc"`
Maximum error in density `(Deltad)/(d)xx100=(Deltam)/(m)xx100+(DeltaV)/(V)xx100`
`=(0.01)/(2.42)xx100+(0.1)/(4.7)xx100=0.413%+2.127%`
`"Maximum error density "=2.54%`