A wire has a mass 0.3 0.003 gram, radius 0.5 0.005 ~mm and length 6 0.06 ~cm . The maximum percentage error in the measurement of its density is

Step-by-step solution

The density of a cylinder is given by = M / ( r^2 L) , where M is mass, r is radius, and L is length. For error propagation in a function of the form X = A^a B^b C^c , the maximum fractional error is X / X = a ( A / A) + b ( B / B) + c ( C / C) . Rewriting density as M^1 r⁻² L⁻¹ with being constant, the percentage error is 100 % = (1 M M + 2 r r + 1 L L ) 100 % . Substituting the reported errors, each term has 1% error: M M = 1 % , r r = 1 % , L L = 1 % . Therefore, the percentage error is (1 % + 2 1 % + 1 %) = 4 %