Question

If the formula for a physical quantity is
ab3
X=
and if the percentage error
1/3 d2
C
in the measurements of a, b, c and d
are 2%, 3%, 3% and 4% respectively.
Calculate percentage error in X.​

Answer 1

Correct Question -

If the formula for a physical quantity is

X = ab³cd² . If the percentage error in the measurements of a , b , c and d are 2% , 3% , 3% and 4% respectively.

Calculate percentage error in X.

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Answer -

If X = $\bf a^nb^mc^pd^q$

then the percentage error in measurement of x =

$\bf n \times a\% + m \times b\% + p\times c\% + q \times d\%$

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Here -

$x = ab^3cd^2$

Percentage error in a = 2%

Percentage error in b = 3%

Percentage error in c = 3%

Percentage error in d = 4%

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Percentage error in x =

$\bf 1 × 2\% + 3 × 3\% + 1 × 3\% + 2 × 4\%$

$\bf =(2 + 9 + 3 + 8)\%$

$\bf = 22 \%$

The percentage error in the measurement of x is 22%.

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Thanks

Answer 2

Correct Question -

If the formula for a physical quantity is

X = ab³cd² . If the percentage error in the measurements of a , b , c and d are 2% , 3% , 3% and 4% respectively.

Calculate percentage error in X.

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Answer -:

$If \:X = \bf a^nb^mc^pd^q$

then the percentage error in measurement of x =

$n ×a% + m ×b% + p×c% + q × d$

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Here -

$x = ab^3cd^2x$

Percentage error in a = 2%

Percentage error in b = 3%

Percentage error in c = 3%

Percentage error in d = 4%

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Percentage error in x =

1 × 2% + 3 × 3% + 1 × 3% + 2 × 4

=(2 + 9 + 3 + 8)%

= 22 %

The percentage error in the measurement of x is 22%.

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