the measure of mass and volume of body are 2.00g and 5.0cm^3 resp. with possible error of 0.01g and 0.1cm^3. what would be the maximum permissible error in its density?
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Answered by
15
The density is given by
d=mV∣∣∆dd∣∣=∣∣∆mm∣∣+∣∣∆VV∣∣where m=2.00g, ∆m=0.01g, V=5cc and ∆V=0.1cc so percentage error in density will be∣∣∆dd∣∣×100%=(0.012+0.15)×100=0.025×100=2.5%
Answered by
40
Density (d) = mass ( m)/volume (V)
d = m/v
d = 2/5 g/cm³
= 0.4 g/cm³
for error ,
∆d/d = ∆m/m + ∆v/v
∆d = { 0.01/2 + 0.1/5 }× 0.4
= 0.01
hence,
∆d = 0.01
relative error = ∆d/d
= 0.01/0.4
= 0.1/4
% error =100 × relative error
= 0.1/4 × 100
= 2.5 %
d = m/v
d = 2/5 g/cm³
= 0.4 g/cm³
for error ,
∆d/d = ∆m/m + ∆v/v
∆d = { 0.01/2 + 0.1/5 }× 0.4
= 0.01
hence,
∆d = 0.01
relative error = ∆d/d
= 0.01/0.4
= 0.1/4
% error =100 × relative error
= 0.1/4 × 100
= 2.5 %
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