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A physical quantity X depends upon four other quantities a, b, c, and d as evident from the relation $X = a^{2} b^{3} c^{5 / 2} d^{- 2}$ . The respective percentage errors in the measurement of a, b, c and d are known to be 1%, 2%,2% and 4%. Calculate the final error in the quantity X.

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17%

21%

15%

23%

answer is C.

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Detailed Solution

As $X = a^{2} b^{3} c^{5 / 2} d^{- 2}$

The percentage error in X is $\frac{ΔX}{X} \times 100$

$= [2 (\frac{Δ a}{a}) + 3 (\frac{Δ b}{b}) + \frac{5}{2} (\frac{Δ c}{c}) + 2 (\frac{Δ d}{d})] \times 100$

$\begin{array}{l} = 2 \times 1 % + 3 \times 2 % + \frac{5}{2} \times 2 % + 2 \\ \times 4 % = 21 % \end{array}$

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