Question

A screw gauge has a pitch of 0.1 mm and 100 divisions on its circular scale. When its both jaws touch, the fifth division of its circular scale coincides with zero. When a sphere is placed between the jaws, the reading of the linear scale is 5 mm and the 50th division of the circular scale coincides with zero of the main scale. Find the diameter of the sphere.

• A. 5.55 mm
• B. 5.45 mm
• C. 5.056 mm
• D. 5.045 mm

Hint:

In screw gauges, the reading is obtained by adding the main scale reading and the circular scale reading, where the circular scale reading is calculated by multiplying the division number with the least count (pitch divided by the number of divisions).

Answer 1

The Correct Option is D

Step 1: Understanding the measurements.
In a screw gauge, the pitch represents the distance moved by the spindle in one complete rotation, while the circular scale provides finer measurement accuracy. In this case, the pitch is \( 0.1 \, \text{mm} \) and the circular scale has 100 divisions. The reading of a screw gauge consists of two components: 1. Main Scale Reading (MSR): The reading on the linear scale, which is \( 5 \, \text{mm} \). 2. Circular Scale Reading (CSR): The additional fractional reading obtained from the circular scale. Here, the 45th division on the circular scale coincides with the reference line.
Step 2: Calculate the least count and circular scale reading.
The least count of the screw gauge is calculated as: \[ \text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions}} = \frac{0.1 \, \text{mm}}{100} = 0.001 \, \text{mm} \] Thus, the circular scale reading is: \[ \text{CSR} = 45 \times 0.001 \, \text{mm} = 0.045 \, \text{mm} \]
Step 3: Calculate the total diameter of the sphere.
The total measurement is obtained by adding the main scale reading and the circular scale reading: \[ \text{Diameter of sphere} = \text{MSR} + \text{CSR} \] \[ \text{Diameter of sphere} = 5 \, \text{mm} + 0.045 \, \text{mm} \] \[ \text{Diameter of sphere} = 5.045 \, \text{mm} \]
Final Answer: \( 5.045 \, \text{mm} \).