A screw gauge advances by 3mm in 6 rotations. There are 50 divisions on circular scale. Find least count of screw gauge

Options

A. 0.001 mm
B. 0.02 mm
C. 0.001 cm
D. 0.01 cm

Answer

To find the least count of the screw gauge, we will follow these steps:

### Step 1: Understand the concept of pitch
The pitch of a screw gauge is defined as the linear advancement of the screw in one complete rotation.

### Step 2: Calculate the pitch
Given that the screw gauge advances by 3 mm in 6 rotations, we can calculate the pitch using the formula:
\[ \text{Pitch} = \frac{\text{Total Advancement}}{\text{Number of Rotations}} = \frac{3 \text{ mm}}{6} = 0.5 \text{ mm} \]

### Step 3: Identify the number of divisions on the circular scale
The problem states that there are 50 divisions on the circular scale.

### Step 4: Calculate the least count
The least count (LC) of the screw gauge can be calculated using the formula:
\[ \text{Least Count} = \frac{\text{Pitch}}{\text{Number of Divisions}} = \frac{0.5 \text{ mm}}{50} \]
Calculating this gives:
\[ \text{Least Count} = 0.01 \text{ mm} \]

### Step 5: Convert the least count to centimeters
Since the options provided are in centimeters, we convert 0.01 mm to centimeters:
\[ 0.01 \text{ mm} = 0.001 \text{ cm} \]

### Final Answer
Thus, the least count of the screw gauge is:
\[ \text{Least Count} = 0.001 \text{ cm} \]