The length of a cylinder is measured as 5 cm using a vernier calipers of least count 0.1 mm. The percentage error is

Options

A. 0.005
B. 0.02
C. 0.2
D. 0.002

Answer

To find the percentage error in the measurement of the length of a cylinder using a vernier caliper, we can follow these steps:

### Step 1: Identify the given values
- Length of the cylinder (L) = 5 cm
- Least count of the vernier caliper (ΔL) = 0.1 mm

### Step 2: Convert the length from centimeters to millimeters
Since the least count is given in millimeters, we should convert the length from centimeters to millimeters:
- 1 cm = 10 mm
- Therefore, 5 cm = 5 × 10 mm = 50 mm

### Step 3: Calculate the absolute error
The absolute error in the measurement is equal to the least count of the instrument:
- Absolute error (ΔL) = 0.1 mm

### Step 4: Calculate the percentage error
The formula for percentage error is given by:
\[ \text{Percentage Error} = \left( \frac{\Delta L}{L} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Error} = \left( \frac{0.1 \text{ mm}}{50 \text{ mm}} \right) \times 100 \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \text{Percentage Error} = \left( \frac{0.1}{50} \right) \times 100 = 0.002 \times 100 = 0.2\% \]

### Final Answer
The percentage error in the measurement of the length of the cylinder is **0.2%**.

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