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

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

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Density = mass/ pi r*r*l
%error = 1 + 2+ 1
= 4%

Regards
Khimraj
3007 Points
4 years ago
your answer is "4%"
___________
Explainatioan =>
______
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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