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If the percentage errors of A,B,and C ar...

If the percentage errors of `A,B,and C are a, b, and c,` respectively ,then the total percentage error in the product `ABC` is

A

abc

B

`a + b+c`

C

`ab + bc+ ac`

D

`(a)/(b) +(b)/(c)+(c)/(a)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(Delta(ABC))/(ABC)=(DeltaA)/(A)+(DeltaB)/(A)+(DeltaC)/(C)=a+b+c`
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ALLEN -ERROR AND MEASUREMENT-Part-2(Exercise-1)
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  4. The diameter of a wire is measured with a screw gauge having least cou...

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  8. When a copper sphere is heated, maximum per- centage change will be ob...

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  9. The period of oscillation of a simple pendulum in the experiment is re...

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  10. The significant digits in 200.40 are

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  11. A scientist performs an experiment in order to measure a certain physi...

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  12. A physical quantity X is represented by X = (M^(x) L^(-y) T^(-z). The ...

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  13. If error in measuring diameter of a circle is 4% the error in circumfe...

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  14. A wire has a mass (0.3+-0.003)g, radius (0.5+-0.005)mm and length (6+-...

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  15. The length of a cylinder is measured with a metre rod having least cou...

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  16. The volume of a sphere is .176 m^3 What will be the volume of 25 such ...

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  17. What is the fractional error in g calculated form T=2pisqrt(l//g) ? Gi...

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  18. The resistance R = V//i, where V = 100 +- 5 V and I = 10+- 0.2 A. What...

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  19. The length, breadth and thickness of a strip are (10.0+-0.1)cm,(1.00+-...

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  20. The internal and external diameters of a hollow cylinder are measured ...

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