Question

A wire has a mass 0.30.003 g,0.30.003 g, radius 0.50.005 mm0.50.005 mm and length 60.06 cm60.06 cm. The maximum percentage error in measurement of its density is :

Answer 1

Since density is mass÷volume,

For a cylinder it becomes- mass÷(pi×radius^2×length)

Relative percent errors for-

Mass-0.003÷0.3×100=1%

Radius^2-2×0.005÷0.5×100=2%

Length-0.06÷0.6×100=1%

THE UNITS CANCEL THEMSELVES FROM THE NUMERATOR AND DENOMINATOR.

therefore,

maximum percentage error in density-1%+2%+1%=4%

so, the answer is 4%

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