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 callipers 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. `+-0.2cm^(2)`
B. `+-0.1cm^(2)`
C. `+-0.3cm^(2)`
D. zero

Answer

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

### Step 1: Identify the given values
- Length (L) = 10.0 cm
- Width (W) = 1.00 cm
- Least count of the meter scale (for length) = 0.1 cm
- Least count of the vernier calipers (for width) = 0.01 cm

### Step 2: Determine the absolute errors
- The absolute error in length (ΔL) is equal to the least count of the meter scale:
\[ \Delta L = 0.1 \, \text{cm} \]
- The absolute error in width (ΔW) is equal to the least count of the vernier calipers:
\[ \Delta W = 0.01 \, \text{cm} \]

### Step 3: Calculate the area of the rectangle
The area (A) of the rectangle is given by:
\[ A = L \times W = 10.0 \, \text{cm} \times 1.00 \, \text{cm} = 10.0 \, \text{cm}^2 \]

### Step 4: Use the formula for the maximum permissible error in area
The formula for the relative error in area (ΔA) is given by:
\[ \frac{\Delta A}{A} = \frac{\Delta L}{L} + \frac{\Delta W}{W} \]
Substituting the values, we get:
\[ \frac{\Delta A}{10.0} = \frac{0.1}{10.0} + \frac{0.01}{1.00} \]

### Step 5: Calculate the individual terms
Calculating each term:
\[ \frac{\Delta L}{L} = \frac{0.1}{10.0} = 0.01 \]
\[ \frac{\Delta W}{W} = \frac{0.01}{1.00} = 0.01 \]

### Step 6: Combine the relative errors
Now, adding these two relative errors:
\[ \frac{\Delta A}{10.0} = 0.01 + 0.01 = 0.02 \]

### Step 7: Calculate the maximum permissible error in area
To find ΔA:
\[ \Delta A = A \times \frac{\Delta A}{A} = 10.0 \, \text{cm}^2 \times 0.02 = 0.2 \, \text{cm}^2 \]

### Conclusion
The maximum permissible error in the area measurement is:
\[ \Delta A = 0.2 \, \text{cm}^2 \]

### Final Answer
The maximum permissible error in area measurement is **0.2 cm²**.

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