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The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is (x/(100))%. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is ______

Asked in JEE Main 6th Sept 1st Shift 2020 · Percentage error in a derived quantity

Answer: 1050

Step-by-step solution

Idea: ρ=m/(π/6d³), so the diameter enters cubed.

(Δρ)/ρ=(Δ m)/m+3(Δ d)/d

=6.0%+3(1.5%)=6.0%+4.5%=10.5%.

Given x/(100)=10.5, so x=1050.

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