Given: \(Q = \frac{a^4 b^3}{c^2}\)
The percentage error in \( Q \) can be calculated using the rule for propagation of errors in multiplication and division.
Step 1. Calculate the fractional error in \( Q \):
\(\frac{\Delta Q}{Q} = 4 \frac{\Delta a}{a} + 3 \frac{\Delta b}{b} + 2 \frac{\Delta c}{c}\)
Step 2. Substitute the given percentage errors:
\(\frac{\Delta Q}{Q} \times 100 = 4 \left( \frac{\Delta a}{a} \times 100 \right) + 3 \left( \frac{\Delta b}{b} \times 100 \right) + 2 \left( \frac{\Delta c}{c} \times 100 \right)\)
\(= 4 \times 3\% + 3 \times 4\% + 2 \times 5\%\)
\(= 12\% + 12\% + 10\%\)
Step 3. Calculate the total percentage error in \( Q \):
\(\text{Percentage error in } Q = 12\% + 12\% + 10\% = 34\%\)
Thus, the percentage error in \( Q \) is 34%.
The Correct Answer is: 34%
If \( T = 2\pi \sqrt{\frac{L}{g}} \), \( g \) is a constant and the relative error in \( T \) is \( k \) times to the percentage error in \( L \), then \( \frac{1}{k} = \) ?