The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is x 100 % .…

The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is x100%. If the relative errors in measuring the mass and the diameter are 6.0% and 1.5% respectively, the value of x is -

Solution

ρ=m43πd23

ρ=6mπd3

taking log

ℓnρ=ℓnm-3ℓnd

Maximum error by differentiation

dρρ=dmm+3ddd

dpρ=6+3×1.5

=10.5%=1050100%

Ans. x = 1050

Asked in: JEE Main 2020 (06 Sep Shift 1)

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