Mass of a sphere of radius r=10.00 cm is 30.000 g if measured values are expressed upto the correct significant figures then maximum fractional error in calculation of density of the sphere is

Options

A. `3xx10^(-5)`
B. `3.3xx10^(-3)`
C. `3.033xx10^(-3)`
D. `3.03xx10^(-5)`

Answer

C

Explanation

`rho=(m)/((4)/(3)pir^(3))implies(Deltarho)/(rho)=(Deltam)/(m)+(3Deltar)/(r)`
`implies(Deltarho)/(rho)=(0.001)/(30)+(3xx0.01)/(10)`
`(Deltarho)/(rho)=3.3xx10^(-5)+3xx10^(-3)`
`(Deltarho)/(rho)=0.033xx10^(-3)+3xx10^(-3)`
`(Deltarho)/(rho)=3.033xx10^(-3)`