A physical quantity A is dependent on other four physical quantities p,q,r and s as given by `A=(sqrt(pq))/(r^(2)s^(3))`. The percentage error of measurement in p,q,r and s are 1%,3%,0.5% and 0.33% respectively, then the maximum percentage error in A is

Options

A. 0.02
B. 0
C. 0.04
D. 0.03

Explanation

To find the maximum percentage error in the physical quantity \( A \) given by the formula

\[ A = \frac{\sqrt{pq}}{r^2 s^3} \]

we will use the method of error propagation. The percentage error in a quantity can be calculated using the formula:

\[ \frac{\Delta A}{A} \times 100 = \text{(percentage error in p)} + \text{(percentage error in q)} + 2 \times \text{(percentage error in r)} + 3 \times \text{(percentage error in s)} \]

### Step 1: Identify the percentage errors
We are given the following percentage errors for the quantities \( p, q, r, \) and \( s \):
- Percentage error in \( p \) = 1%
- Percentage error in \( q \) = 3%
- Percentage error in \( r \) = 0.5%
- Percentage error in \( s \) = 0.33%

### Step 2: Substitute the errors into the formula
Now, substituting these values into the error propagation formula:

\[ \frac{\Delta A}{A} \times 100 = 1\% + 3\% + 2 \times 0.5\% + 3 \times 0.33\% \]

### Step 3: Calculate each term
Calculating each term:
- The contribution from \( p \) = 1%
- The contribution from \( q \) = 3%
- The contribution from \( r \) = \( 2 \times 0.5\% = 1\% \)
- The contribution from \( s \) = \( 3 \times 0.33\% = 0.99\% \)

### Step 4: Sum the contributions
Now, summing these contributions together:

\[ 1\% + 3\% + 1\% + 0.99\% = 6\% - 0.01\% = 5.99\% \]

### Step 5: Finalize the maximum percentage error
Thus, the maximum percentage error in \( A \) is approximately:

\[ \frac{\Delta A}{A} \times 100 \approx 5.99\% \]

### Conclusion
The maximum percentage error in \( A \) is approximately **5.99%**.

---