The density of a solid metal sphere is 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 % respe

Question

The density of a solid metal sphere is 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 -

TestHub · Accepted Answer

ρ = m 4 3 π d 2 3 ρ = 6 m π d 3 taking log ℓ n ρ = ℓ n m - 3 ℓ n d Maximum error by differentiation d ρ ρ = d m m + 3 d d d d p ρ = 6 + 3 × 1 . 5 = 10 . 5 % = 1050 100 % Ans. x = 1050

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