The dimensions of a rectangular block measured with a vernier callipers having least count of `0.1mm` is `5mmxx10mmxx5mm`. The maximum percentage error in measurement of volume of the blcok is

Options

A. `5%`
B. `10%`
C. `15%`
D. `20%`

Explanation

To find the maximum percentage error in the measurement of the volume of a rectangular block measured with a vernier caliper, we can follow these steps:

### Step 1: Understand the dimensions and the least count
The dimensions of the rectangular block are given as:
- Length (L) = 5 mm
- Breadth (B) = 10 mm
- Height (H) = 5 mm

The least count of the vernier caliper is given as 0.1 mm.

### Step 2: Calculate the volume of the block
The volume (V) of a rectangular block is calculated using the formula:
\[ V = L \times B \times H \]
Substituting the values:
\[ V = 5 \, \text{mm} \times 10 \, \text{mm} \times 5 \, \text{mm} = 250 \, \text{mm}^3 \]

### Step 3: Determine the absolute error in each dimension
The absolute error in each measurement due to the least count is:
- For Length (ΔL) = 0.1 mm
- For Breadth (ΔB) = 0.1 mm
- For Height (ΔH) = 0.1 mm

### Step 4: Calculate the relative error for each dimension
The relative error for each dimension is given by:
\[ \text{Relative Error} = \frac{\text{Absolute Error}}{\text{Measured Value}} \]

Calculating for each dimension:
- For Length:
\[ \frac{\Delta L}{L} = \frac{0.1 \, \text{mm}}{5 \, \text{mm}} = 0.02 \]
- For Breadth:
\[ \frac{\Delta B}{B} = \frac{0.1 \, \text{mm}}{10 \, \text{mm}} = 0.01 \]
- For Height:
\[ \frac{\Delta H}{H} = \frac{0.1 \, \text{mm}}{5 \, \text{mm}} = 0.02 \]

### Step 5: Calculate the total relative error in volume
The total relative error in volume is the sum of the relative errors of each dimension:
\[ \text{Total Relative Error} = \frac{\Delta L}{L} + \frac{\Delta B}{B} + \frac{\Delta H}{H} \]
Substituting the values:
\[ \text{Total Relative Error} = 0.02 + 0.01 + 0.02 = 0.05 \]

### Step 6: Convert relative error to percentage error
To find the percentage error, multiply the total relative error by 100:
\[ \text{Percentage Error} = \text{Total Relative Error} \times 100 = 0.05 \times 100 = 5\% \]

### Final Answer
The maximum percentage error in the measurement of the volume of the block is **5%**.

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