Number 4. Doing a Propagated uncertainty problem and need help with deriving the

Question

Number 4. Doing a Propagated uncertainty problem and need help with deriving the expression. The equation is Density, m/v, and the volume shape is a cylinder.

ing hisity iomndu Tor yodt d bt cite the hmecal value of the density and record it with the proper units and significant figures. The formula should only contain variables tha t we re measure 049 Derive an expression for the uncertainty in density. The expression should only contain variables that were mcasured dircctly. Show all steps, including differentiations ot lo Using the symbolic expression derived above, insert the measured data and compute the numerical value of the propagated uncertainty and present it along with the units. Make sure it is to the same decimal precision as your calculated density 5. .3

Explanation / Answer

given
the volume is a cylinder of radius R, height H
Given mass = M
now, density, rho = M/Volume
but Volume = pi*R^2*H
so, rho = M/pi*R^2*H
now, if error in H is dH, error in R is dR, error in M is dM
then
d(rho)/rho = sqroot((dM/M)^2 + (2*dR/R)^2 + (dH/H)^2)
where rho = M/pi*R^2*H
and d(rho) is error in rho

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