The percentage errors in a - b - c are - 1 - - 3 - and - 2 - respectively- The percentage error in x - ab 2- c 3 can be A- - 13 -B- - 7 -C- - 4 -D- - 1 -

The correct option is A ±13%x=ab^2/c^3⇒Δ x/x=Δ a/a+2Δ b/b+3Δ c/c Percentage error in = ± [1+2(3)+3(2) ]%=±13% ...

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Standard XII

Physics

Thermal Expansion

The percentag...

Question

The percentage errors in a, b, c are $\pm 1 %, \pm 3 %$ and $\pm 2 %$ respectively. The percentage error in $x = \frac{a b^{2}}{c^{3}}$ can be

\pm 13 %

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\pm 7 %

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\pm 4 %

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\pm 1 %

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Solution

The correct option is A $\pm 13 %$
$x = \frac{a b^{2}}{c^{3}} \Rightarrow \frac{Δ x}{x} = \frac{Δ a}{a} + 2 \frac{Δ b}{b} + 3 \frac{Δ c}{c}$

Percentage error in

= $\pm [1 + 2 (3) + 3 (2)] % = \pm 13 %$

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The percentage errors in a, b, c are ±1%, ±3% and ±2% respectively. The percentage error in x=ab2c3 can be

The correct option is A ±13%x=ab2c3⇒Δxx=Δaa+2Δbb+3Δcc Percentage error in = ± [1+2(3)+3(2)]%=±13%

The percentage errors in a, b, c are $\pm 1 %, \pm 3 %$ and $\pm 2 %$ respectively. The percentage error in $x = \frac{a b^{2}}{c^{3}}$ can be

The correct option is A $\pm 13 %$
$x = \frac{a b^{2}}{c^{3}} \Rightarrow \frac{Δ x}{x} = \frac{Δ a}{a} + 2 \frac{Δ b}{b} + 3 \frac{Δ c}{c}$

Percentage error in

= $\pm [1 + 2 (3) + 3 (2)] % = \pm 13 %$