Mathematics in Physics

JEE Main level, single correct, medium

108 of 121

Question 108 of 121

The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are 1.51.5% and 11%, respectively, the maximum error in determining the density is:

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Answer: (D) 4.54.5%

ρ=ML3\rho =\dfrac{M}{{L}^{3}}⇒Δρρ=ΔMM+3ΔLL\Rightarrow \dfrac{\Delta \rho }{\rho }=\dfrac{\Delta M}{M}+\dfrac{3\Delta L}{L}⇒Δρρ×100=1.5+3×1\Rightarrow \dfrac{\Delta \rho }{\rho }\times 100=1.5+3\times 1
% relative error,=4.5=4.5%

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