Calculate the density of earth and its density error
d=m/v
where m = 6.00*10^24kg
and v = (4/3)(pi)(6359000)^3
= 1.07709...*10^21 m^3
therefore d=6.00*10^24/1.07709...*10^21 m^3
d = 5570.5254...kg/m^3
using the sig fig rule, in division and multiplication take the least decimal value and round the answer to that...
therefore d=5.57*10^3kg/m^3
then for error analysis, i did the below..
since i need the error analysis for the volume i used the formula
deltaV = n(deltaR / R), where r is the radius and n is the coefficient of the power
therefore deltaV = 3(20000/6359000)
delta V = 3.145148...*10^-3
then to calculate the delta D i used the formula:
deltaD = D(sqrt[(deltaM/M)^2 + (deltaV/V)^2])
therefore delta D = 5.57*10^3(sqrt[(5.00*10^22/6.00*10^24)^2/(3.145148*10^-3/1.07709*10^21)^2])
delta D = 46.42104...
I re did this calculations and i am getting a different value, please help me out and check whether it is correct or not
The density calculation looks fine and I would agree with the 3 sig figs in the answer as the mass is to 3 sig figs.
I am not entirely sure what you are doing with the error estimation, however
the delta V seems small
As a crude estimate the error in m is say +/- 0.01x10^24 or 1.7%, which swamps the error in V which is about 0.05%
Thus the error in the density will be dominated by error in the mass, so the error in the density will be +/-
5.57x10^3 x 1.7/100 = 95 kg m^-3
which will be an over estimate.
so your value of 46 is of the correct magnitude
Let's go through the calculations to help identify any errors:
1. Calculating the density:
The mass (m) is given as 6.00 x 10^24 kg.
The volume (v) is calculated as (4/3)π(6359000)^3, which is approximately 1.07709 x 10^21 m^3.
Using the formula d = m/v, substituting the values, we have 6.00 x 10^24 kg / 1.07709 x 10^21 m^3 = 5570.5254 kg/m^3.
Using significant figures, we round to three significant figures, giving us the density as 5.57 x 10^3 kg/m^3.
2. Calculating the error in volume:
The formula for the error in volume (deltaV) is given as deltaV = n(deltaR / R), where deltaR is the uncertainty in the radius.
Substituting the values, we have deltaV = 3(20000 / 6359000) = 3.145148 x 10^-3 m^3.
3. Calculating the error in density:
The formula for the error in density (deltaD) is given as deltaD = D * sqrt((deltaM/M)^2 + (deltaV/V)^2).
Substituting the values, we have deltaD = 5.57 x 10^3 * sqrt((5.00 x 10^22 / 6.00 x 10^24)^2 + (3.145148 x 10^-3 / 1.07709 x 10^21)^2).
Calculating this expression, we get deltaD = 46.42104.
Therefore, based on the calculations provided, the density of Earth is approximately 5.57 x 10^3 kg/m^3 with an error of approximately 46.42104 kg/m^3.