Dimensions of physical quantities

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Question

A physical quantity P is described by the relation $P = a^{1 / 2} b^{2} c^{3} d^{- 4}$ . If the relative errors in the measurement of a, b, c and d respectively, are 2%,1%, 3% and 5%, then the percentage error in P will be_______ %

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Solution

Here, $P = a^{1 / 2} b^{2} c^{3} d^{- 4}$
$\frac{ΔP}{P} = \frac{1}{2} \frac{Δa}{a} + 2 \frac{Δb}{b} + 3 \frac{Δc}{c} + 4 \frac{Δd}{d}$
or $(\frac{ΔP}{P} \times 100) % = (\frac{1}{2} \frac{Δa}{a} + 2 \frac{Δb}{b} + 3 \frac{Δc}{c} + 4 \frac{Δd}{d}) \times 100 %$
$\Rightarrow$ Percentage error in P
$= (\frac{1}{2} \times 2 + 2 \times 1 + 3 \times 3 + 4 \times 5) \times 100 = 32 %$

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Dimensions of physical quantities

Remember concepts with our Masterclasses.

A physical quantity P is described by the relation P=a1/2b2c3d−4. If the relative errors in the measurement of a, b, c and d respectively, are 2%,1%, 3% and 5%, then the percentage error in P will be_______ %

Here, P=a1/2b2c3d−4ΔPP=12Δaa+2Δbb+3Δcc+4Δddor ΔPP×100%=12Δaa+2Δbb+3Δcc+4Δdd×100%⇒ Percentage error in P=12×2+2×1+3×3+4×5×100=32%

Ready to Test Your Skills?

free study material

A physical quantity P is described by the relation $P = a^{1 / 2} b^{2} c^{3} d^{- 4}$ . If the relative errors in the measurement of a, b, c and d respectively, are 2%,1%, 3% and 5%, then the percentage error in P will be_______ %