A physical quantity P is described by the relation P=a^1/2 b² c³ d⁻⁴. If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be

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(4) 32%. Idea: every exponent weights its error in magnitude; the negative exponent on d still adds. (Δ P)/P=1/2(Δ a)/a+2(Δ b)/b+3(Δ c)/c+4(Δ d)/d =1/2(2%)+2(1%)+3(3%)+4(5%) =1%+2%+9%+20%=32%. The printed key gives 8%, which no reading of the exponents produces; the derivation stands. See DEFECTS.

A physical quantity P is described by the relation P=a^1/2 b² c³ d⁻⁴. If the relative errors in the measurement of a, b, c and d respectively, are 2%, 1%, 3% and 5%, then the relative error in P will be

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Why the other options are wrong