Question

To measure the density of a rectangular object, an experimenter measures the object's volume and mass. The volume is given by the formula V = LWH, where L is the length, W is the width, and H is the height. The density is given by p = m/V, where m is the object's mass. If the measurement of the mass is uncertain by 2%, and each of L, W and H is uncertain by 4%, what is the uncertainty, in percent, of the density?

Answer 1

error in density is given by($\Delta$p/p)=($\Delta$m/m) + ($\Delta$V/V)

But ($\Delta$V/V) = ($\Delta$L/L) + ($\Delta$W/W) + ($\Delta$H/H)

So ($\Delta$p/p)=($\Delta$m/m) + ($\Delta$L/L) + ($\Delta$W/W) + ($\Delta$H/H)

For per centage error ($\Delta$p/p) x 100 = [ ($\Delta$m/m) + ($\Delta$L/L) + ($\Delta$W/W) + ($\Delta$H/H)] x 100

= [ 0.02 + 0.04 + 0.04 + 0.04 ] x 100

= 1.4%