The mass of a body is `20.000 g` and its volume is `10.00 cm^(3)`. If the measured values are expressed to the correct significant figures , the maximum error in the value of density is

Options

A. `0.001 g cm^(-3)`
B. `0.010 g cm^(-3)`
C. `0.100 g cm^(-3)`
D. None of these

Answer

D

Explanation

Maximum error in measuring mass ` = 0.001 g` , because least count is `0.001 g `. Similarly , maximum error in measuring volume is `0.01 cm^(3)`.
`( Delta rho)/( rho) = ( Delta M) /(M) + ( Delta V)/(V) = ( 0.001) /( 20.000) + ( 0.01)/( 10.00)`
` = ( 5 xx 10^(-5)) + ( 1 xx 10^(-3)) = 1.05 xx 10^(-3)`
` Delta rho = ( 1.05 xx 10^(-3) xx rho `
`= 1.05 xx 10^(-3) xx ( 20.000) /( 10.00) = 0.002 g cm^(-3)`