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Physics Notes on Units and Measurement for CBSE Class 11

Jun 16, 2017 ... Class 11 Physics notes on Units & Measurement (Chapter 2 of 11th ... Error, Relative Error and Percentage Error, Combination of Errors, ... The result of every measurement by any measuring instrument contains some uncertainty. ... The relative error in a physical quantity raised to the power k is the k times ...

For more information, see Physics Notes on Units and Measurement for CBSE Class 11

The relative error in a physical quantity raised to the power k is equal to k times the individual quantity's relative error.

Z = \frac{A^p B^q}{C^r}

\frac{\Delta Z}{Z} = p \frac{\Delta A}{A} + q \frac{\Delta B}{B} + r \frac{\Delta C}{C}   

Percentage error = \frac{\text{ absolute error }}{\text{ measurement }} 100%

Percentage error in the quantity P = \frac{\Delta P}{P} * 100

Given that

Physical quantity P = \frac{a^3 b^3}{\sqrt{c}d} , where, a, b, c and d  are observables

The percentage errors of observables \frac{\Delta a}{a}* 100 = 1%

\frac{\Delta b}{b} * 100 = 3%

\frac{\Delta c}{c} * 100 = 4%

\frac{\Delta d}{d} * 100= 2%

Step 1: Finding the percentage error

Physical quantity, P = \frac{a^3 b^3}{\sqrt{c}d}

P = \frac{a^3 b^3}{c^{\frac{1}{2}}d}

Error when a calculated quantity is raised to a power

Relative error \frac{\Delta P}{P} = 3 \frac{\Delta a}{a} + 3\frac{\Delta b}{b} + \frac{1}{2} \frac{\Delta c}{c} + \frac{\Delta d}{d}

Percentage error   \frac{\Delta P}{P} * 100 = 3 \frac{\Delta a}{a} * 100 + 3 \frac{\Delta b}{b} * 100 + \frac{1}{2} \frac{\Delta c}{c} * 100 + \frac{\Delta d}{d} * 100

\frac{\Delta P}{P} * 100 = =  3 * 1% + 3 * 3% + \frac{1}{2} 4% + 2%

= 3 % + 9 % + 2% + 2%

= 13%

Hence, Percentage error of the quantity, P = 13%    

Given value of the quantity P, = 3.763

Rounding the quantity P = 3.8