The least count of screw gauge is `(1)/(100)mm` and the pitch of the screw is `1mm`. The maximum percentage error of the instrument is

Options

A. `5%`
B. `2%`
C. `1%`
D. `10%`

Explanation

To find the maximum percentage error of the screw gauge, we can follow these steps:

### Step 1: Understand the Given Data
- Least count of the screw gauge = \( \frac{1}{100} \) mm
- Pitch of the screw = 1 mm

### Step 2: Determine the True Value
The true value for the measurement using the screw gauge is equal to the pitch, which is 1 mm.

### Step 3: Calculate the Error in Measurement
The error in measurement is equal to the least count of the screw gauge. Therefore, the error is:
\[ \text{Error} = \text{Least Count} = \frac{1}{100} \text{ mm} \]

### Step 4: Calculate the Maximum Percentage Error
The formula for percentage error is given by:
\[ \text{Percentage Error} = \left( \frac{\text{Error}}{\text{True Value}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Error} = \left( \frac{\frac{1}{100} \text{ mm}}{1 \text{ mm}} \right) \times 100 \]

### Step 5: Simplify the Calculation
\[ \text{Percentage Error} = \left( \frac{1}{100} \right) \times 100 = 1\% \]

### Conclusion
The maximum percentage error of the instrument is \( 1\% \).

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