Question

Let the physical quantity be \( x = \frac{a^3b^2}{c} \). If the percentage error in the measurement of \( a \), \( b \), and \( c \) is 2%, 3%, and 4% respectively, then the percentage error in the measurement of \( x \) is:

• A. 14%
• B. 7%
• C. 28%
• D. 21%

Hint:

When calculating percentage errors, remember to multiply the individual errors by the powers of the quantities involved in the formula.

Answer 1

The Correct Option is A

Step 1: Formula for Percentage Error.
The percentage error in a physical quantity is the sum of the individual percentage errors in the quantities used to compute it, weighted according to their powers. Here, we have: \[ \text{Percentage error in } x = 3 \times (\text{Percentage error in } a) + 2 \times (\text{Percentage error in } b) + (\text{Percentage error in } c) \] Substituting the values: \[ \text{Percentage error in } x = 3 \times 2 + 2 \times 3 + 1 \times 4 = 6 + 6 + 4 = 14% \] Step 2: Final Answer.
Thus, the percentage error in \( x \) is 14%.