The length of a rectangular plate is measured by a meter scale and is found to be ` 10.0 cm`. Its width is measured by vernier calipers as `1.00 cm`. The least count of the meter scale and vernier calipers are `0.1 cm and 0.01 cm` respectively. Maximum permissibe error in area measurement is.

Options

A. `(a)+- 2 %`
B. `(b) +- 1%`.
C. `(c)+- 3%`.
D. (d)zero.

Explanation

To find the maximum permissible error in the area measurement of a rectangular plate, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Measurements**:
- Length (L) = 10.0 cm (measured with a meter scale)
- Width (W) = 1.00 cm (measured with vernier calipers)

2. **Identify the Least Counts**:
- Least Count of Meter Scale (LC_L) = 0.1 cm
- Least Count of Vernier Calipers (LC_W) = 0.01 cm

3. **Calculate the Absolute Errors**:
- The absolute error in length (ΔL) is equal to the least count of the meter scale:
\[ ΔL = LC_L = 0.1 \, \text{cm} \]
- The absolute error in width (ΔW) is equal to the least count of the vernier calipers:
\[ ΔW = LC_W = 0.01 \, \text{cm} \]

4. **Calculate the Area (A)**:
- The area of the rectangle is given by:
\[ A = L \times W = 10.0 \, \text{cm} \times 1.00 \, \text{cm} = 10.0 \, \text{cm}^2 \]

5. **Calculate the Relative Error in Area**:
- The formula for relative error in area (ΔA/A) is:
\[ \frac{ΔA}{A} = \frac{ΔL}{L} + \frac{ΔW}{W} \]
- Substitute the values:
\[ \frac{ΔA}{A} = \frac{0.1}{10.0} + \frac{0.01}{1.00} \]
- Calculate each term:
\[ \frac{ΔA}{A} = 0.01 + 0.01 = 0.02 \]

6. **Convert to Percentage Error**:
- To find the percentage error, multiply by 100:
\[ \text{Percentage Error} = \frac{ΔA}{A} \times 100 = 0.02 \times 100 = 2\% \]

7. **Conclusion**:
- The maximum permissible error in area measurement is **2%**.