A steel ball of mass 8.2+/-0.2g has a radius of 6.3+/-0.1mm. The density of the ball is found to be 7.8gcm^-3. What is the uncertainty in the density in gcm^-3?
If you could please show some working as well it'd be much appreciated :D!
If you could please show some working as well it'd be much appreciated :D!
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% uncertainty = 'PU' for brevity.
PU of m = 100 x 0.2/8.2 = 2.4%
PU of r = 100x 0.1/6.3 = 1.6%
For multiplication AND division, you add the PUs
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Volume is calculated using r^3 (r x r x r), so PU of volume will be 3 x 1.6 = 4.8%
Density =mass / volume, so PU of density = 4.8 +2.4 = 7.2%
7.2% of 7.8 = 7.8 x 7.2/100 = 0.56 = 0.6
So uncertainty in density is 0.6gcm^-3 (density = 7.8 +/- 0.6) gcm^-3
PU of m = 100 x 0.2/8.2 = 2.4%
PU of r = 100x 0.1/6.3 = 1.6%
For multiplication AND division, you add the PUs
.
Volume is calculated using r^3 (r x r x r), so PU of volume will be 3 x 1.6 = 4.8%
Density =mass / volume, so PU of density = 4.8 +2.4 = 7.2%
7.2% of 7.8 = 7.8 x 7.2/100 = 0.56 = 0.6
So uncertainty in density is 0.6gcm^-3 (density = 7.8 +/- 0.6) gcm^-3