Percentage uncertainty in length and width of a rectangle is 2% and 3%. The total uncertainty in the area of that rectangle is:
Correct answer: B. 5%
- A. 1.5%
- B. 5%
- C. 1%
- D. 6%
Explanation
The following is the solution:Area = length x widthRelative uncertainties are added, when two quantities are multiplied.For addition or subtraction: The uncertainties add up directly.For multiplication or division: The relative uncertainties (expressed as a fraction or percentage) add up directly. To obtain the absolute uncertainty, multiply the combined relative uncertainty by the result of the multiplication or division.For powers or roots: Multiply the absolute uncertainty by the power or root exponent.
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About Measurements
Physical quantities are expressed with SI base and derived units, while measurement limits are described through accuracy, precision, absolute and percentage error, and significant figures. Dimensional analysis checks equations, derives relationships and detects inconsistent units, but it cannot determine numerical constants or distinguish quantities with identical dimensions.
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