Question

a wire has mass of (0.3 +- 0.003) g , a radius of (0.5 +- 0.005)mm and length (6 +- 0.06)cm. Find the percentage error in the measurment of its density.

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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