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A certain body weighs 22.42 g and has a measured volume of 4.7 cc. The possible errors in the measurement of mass and volume are 0.01 g and 0.1 cc. Then the maximum error in the density will be

Asked in CBSE AIPMT 1991 · Percentage error in a derived quantity

Answer: (2) 2%

Step-by-step solution

Given: m=22.42 g with Δ m=0.01 g, V=4.7 cc with Δ V=0.1 cc.

ρ=m/V

(Δρ)/ρ=(Δ m)/m+(Δ V)/V

(0.01)/(22.42)×100=0.045%

(0.1)/(4.7)×100=2.13%

Idea: the coarser measurement dominates; the volume term is nearly fifty times the mass term.

Total =0.045+2.13=2.17≈2%

Why the other options are wrong

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