Notifications
Clear all
1
20/09/2020 2:27 pm
Topic starter
The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is (x/100)%. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is
1 Answer
1
20/09/2020 2:33 pm
ρ = m/{4/3π(d/2)3}
ρ = 6m/πd3
taking log
ℓnρ = ℓnm - 3ℓnd
Maximum error by differentiation
dρ/ρ = dm/m + 3 dd/d
dρ/ρ = 6 + 3 x 1.5
= 10.5% = 1050/100 %
x = 1050