A quantity x is defined as x-a2-b2-c-d- Value of a- b- c and d are reported as a -3 - 0-001- b-5 - 0-0013- c-6 - 0-24 and d-10 - 0-4- Percentage error in x will beA- 2B- 6C- 7D- 4

The correct option is D 4 % error in x =% error in (a^3 b^2)+1/2 error in (c+d) % error in (a^3 b^2)=3a^2 a+2b b/a^3 b^2× 100 % error in (c+3)= c+ d/c+d×100 ...

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Byju's Answer

Standard XII

Physics

Multiplication & Division of Errors

A quantity x ...

Question

A quantity x is defined as $x = \frac{a^{2} - b^{2}}{\sqrt{c + d}}$ . Value of a, b, c and d are reported as a = 3 $\pm$ 0.001, b = 5 $\pm$ 0.0013, c = 6 $\pm$ 0.24 and d = 10 $\pm$ 0.4. Percentage error in x will be

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Solution

The correct option is B
4

$% error in x = % error in (a^{3} - b^{2}) + \frac{1}{2} error in (c + d) % error in (a^{3} - b^{2}) = \frac{3 a^{2} △ a + 2 b △ b}{a^{3} - b^{2}} \times 100 % error in (c + 3) = \frac{△ c + △ d}{c + d} \times 100$

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A quantity x is defined as x=a2−b2√c+d. Value of a, b, c and d are reported as a = 3 ±0.001, b = 5 ±0.0013, c = 6 ±0.24 and d = 10 ± 0.4. Percentage error in x will be

The correct option is B 4 % error in x =% error in (a3−b2)+12 error in (c+d)% error in (a3−b2)=3a2△a+2b△ba3−b2×100% error in (c+3)=△c+△dc+d×100

A quantity x is defined as $x = \frac{a^{2} - b^{2}}{\sqrt{c + d}}$ . Value of a, b, c and d are reported as a = 3 $\pm$ 0.001, b = 5 $\pm$ 0.0013, c = 6 $\pm$ 0.24 and d = 10 $\pm$ 0.4. Percentage error in x will be

The correct option is B
4

$% error in x = % error in (a^{3} - b^{2}) + \frac{1}{2} error in (c + d) % error in (a^{3} - b^{2}) = \frac{3 a^{2} △ a + 2 b △ b}{a^{3} - b^{2}} \times 100 % error in (c + 3) = \frac{△ c + △ d}{c + d} \times 100$