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Standard XII

Physics

Addition & Subtraction of Errors

A physical qu...

Question

A physical quantity x is calculated from $x = a b^{2} / s q r t c$ . Calculate the percentage error in measuring x when the percentage errors in measuring a, b, and c are $4, 2 a n d 3 %$ respectively.

7 %

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9 %

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11 %

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9.5 %

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Solution

The correct option is D $9.5 %$
$x = {a b}^{2} c^{- 1 / 2}$
We know from rules of propagation of error.
$\frac{Δ x}{x} = \frac{Δ a}{a} + \frac{2 Δ b}{b} + \frac{1}{2} \frac{Δ c}{c}$
$\Rightarrow$ $\frac{Δ x}{x} = 4 + 2 \times 2 + \frac{1}{2} \times 3 = 8 + 1.5 = 9.5$ %

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A physical quantity x is calculated from x=ab2/sqrtc. Calculate the percentage error in measuring x when the percentage errors in measuring a, b, and c are 4,2and3% respectively.

The correct option is D 9.5%x=ab2c−1/2We know from rules of propagation of error.Δxx=Δaa+2Δbb+12Δcc⇒ Δxx=4+2×2+12×3=8+1.5=9.5%

A physical quantity x is calculated from $x = a b^{2} / s q r t c$ . Calculate the percentage error in measuring x when the percentage errors in measuring a, b, and c are $4, 2 a n d 3 %$ respectively.

The correct option is D $9.5 %$
$x = {a b}^{2} c^{- 1 / 2}$
We know from rules of propagation of error.
$\frac{Δ x}{x} = \frac{Δ a}{a} + \frac{2 Δ b}{b} + \frac{1}{2} \frac{Δ c}{c}$
$\Rightarrow$ $\frac{Δ x}{x} = 4 + 2 \times 2 + \frac{1}{2} \times 3 = 8 + 1.5 = 9.5$ %