Question

A physical quantity ' \(X\) ' is related to four quantities as \(X = a^2 b^3 c^{5/2} d^{-2}\). The percentage error in 'a', 'b', 'c' and 'd' are \(1%\), \(2%\), \(2%\) and \(4%\) respectively. The percentage error in ' \(X\) ' is.

• A. \(15%\)
• B. \(17%\)
• C. \(21%\)
• D. \(23%\)

Hint:

Always add the products of power and percentage error, regardless of whether the term is in the numerator or denominator.

Answer 1

The Correct Option is C

Step 1: Relative Error Formula
\(\frac{\Delta X}{X} = 2\frac{\Delta a}{a} + 3\frac{\Delta b}{b} + \frac{5}{2}\frac{\Delta c}{c} + 2\frac{\Delta d}{d}\).

Step 2: Calculation
\(% X = 2(1) + 3(2) + \frac{5}{2}(2) + 2(4)\).
\(% X = 2 + 6 + 5 + 8 = 21%\).
Final Answer: (C)