if the errors involved in the measurements of a side and mass of a cube are 3% and 4% respectively ,what is the maximum permissible error in the density of the material?
we know that
density = mass / volume
or
ρ = M/V = M / L3
here,
L = length of each side
so, in terms of percentage errors
(Δρ/ρ) x 100 = [(ΔM/M) x 100] + 3[(ΔL/L) x 100]
given,
percentage error in M = 4%
percentage error in L = 3%
so,
(Δρ/ρ) x 100 = 4% + 3x(3%) = 4% + 9%
thus,
percentage error in density will be
(Δρ/ρ) x 100 = 13%