If diameter and circumference both have an error of 1% , what is the error in va | TestHub

Passage / Comprehension

When numbers having uncertainties or errors are used to compute other numbers, these will be uncertain. It is especially important to understand this when a number obtained from measurements is to be compared with a value obtained from theoretical prediction. Assume a student wants to verify the value of π the ratio of circumference to diameter of a circle. The correct value of ten digits is 3.141592654. He draws a circle and measures its diameter and circumference to its nearest millimeter obtaining the values 135

mm and 424 mm, respectively. Using a calculator he finds π = 3.140740741.

If diameter and circumference both have an error of $1%$ , what is the error in value of $π$ ?

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Answer:

Solution:

$π = \frac{C}{D}$

where $C = 2 π r$ is the circumference and $D = 2 r$ is the diameter.

The fractional uncertainty in $π$ is given by:

$\frac{Δ π}{π} = \frac{Δ C}{C} + \frac{Δ D}{D}$

$\frac{Δ π}{π} = (1% + 1%) = 2%$

Physics - Unit & Dimension Question with Solution | TestHub

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