A physical quantity x depends upon three physical quantities ‘a’, ‘b’ and ‘c’ and they are related by the equationx=ab2c3 . If the errors in measuring ‘a’, ‘b’ and ‘c’ are respectively 4%, 1% and 1% find the maximum possible error in ‘x’.

x=a1/2.b2.c−3∴ Δxxmax×100%=12Δaa×100%+2Δbb×100%+3Δcc×100%=12×4%+2×1%+3×1%=7%

A physical quantity x depends upon three physical quantities ‘a’, ‘b’ and ‘c’ and they are related by the equationx=ab2c3 . If the errors in measuring ‘a’, ‘b’ and ‘c’ are respectively 4%, 1% and 1% find the maximum possible error in ‘x’.

x=a1/2.b2.c−3∴ Δxxmax×100%=12Δaa×100%+2Δbb×100%+3Δcc×100%=12×4%+2×1%+3×1%=7%

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A physical quantity x depends upon three physical quantities ‘a’, ‘b’ and ‘c’ and they are related by the equation $x = \frac{\sqrt{a} b^{2}}{c^{3}}$ . If the errors in measuring ‘a’, ‘b’ and ‘c’ are respectively 4%, 1% and 1% find the maximum possible error in ‘x’.

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$x = {(a)}^{1 / 2} . {(b)}^{2} . {(c)}^{- 3}$

$∴ {(\frac{Δx}{x})}_{\max} \times 100 % = \frac{1}{2} (\frac{Δa}{a}) \times 100 % + 2 (\frac{Δb}{b}) \times 100 % + 3 (\frac{Δc}{c}) \times 100 %$

$= \frac{1}{2} \times 4 % + 2 \times 1 % + 3 \times 1 % = 7 %$

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A physical quantity x depends upon three physical quantities ‘a’, ‘b’ and ‘c’ and they are related by the equationx=ab2c3 . If the errors in measuring ‘a’, ‘b’ and ‘c’ are respectively 4%, 1% and 1% find the maximum possible error in ‘x’.

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A physical quantity x depends upon three physical quantities ‘a’, ‘b’ and ‘c’ and they are related by the equation $x = \frac{\sqrt{a} b^{2}}{c^{3}}$ . If the errors in measuring ‘a’, ‘b’ and ‘c’ are respectively 4%, 1% and 1% find the maximum possible error in ‘x’.