A wire has a mass `0.3+-0.003g`, radius `0.5+-0.005mm` and length `6+-0.06cm`. The maximum percentage error in the measurement of its density is

Options

A. 1
B. 2
C. 3
D. 4

Answer

D

Explanation

(4) `m = rho pi r^(2) l`
`rho = (m)/(pi r^(2) l)`
`(Delta rho)/(rho) = (Delta m)/(m) + 2 (Delta r)/(r ) + (Delta l)/(l)`
`= (0.003)/(0.3) + 2 xx (0.005)/(0.5) + (0.06)/(6)`
`= 0.01 + 0.02 + 0.01`
`= 0.04`
`(Delta rho)/(rho) xx 100 = 4%`