Question

The zero line of the Vernier scale lies between divisions 20 and 21 of the main scale. The 4th Vernier scale division exactly coincides with a main scale division. The 5 divisions of the Vernier scale are equal to 4 divisions of the main scale. If one main scale division is 1 mm, the measured value (in mm) is ........... (Rounded off to one decimal place)}

Hint:

In Vernier scale measurements, the main scale reading is combined with the Vernier scale reading to give the final measurement.

Answer 1

Correct Answer: 20.8

The question involves reading a measurement from a Vernier scale. Given the details: 5 divisions of the Vernier scale equal 4 divisions of the main scale, and one main scale division equals 1 mm.

The relationship between the Vernier scale and main scale is defined as: if 5 Vernier scale divisions (VSD) equal 4 main scale divisions (MSD), one division of the Vernier scale is slightly smaller than one division of the main scale:

VSD = (4/5) MSD = 0.8 mm per VSD

The 4th Vernier scale division coincides with a main scale division, indicating:

4 × VSD = n × MSD

where n is the coinciding main scale division value. Thus,

4 × 0.8 mm = n mm
n = 3.2

This represents the difference between the main scale zero point and the Vernier scale zero point. This discrepancy is called the Vernier constant or least count (LC), calculated as:

LC = 1 MSD - 1 VSD = 1 mm - 0.8 mm = 0.2 mm

The zero of the Vernier lies between divisions 20 and 21 on the main scale, signifying the base measurement as:

Base measurement = 20 mm

The coinciding division (4th Vernier) alters the reading by adding the Vernier coincidence value:

Measured value = Base measurement + (Number of Vernier divisions × LC)
Measured value = 20 mm + (4 × 0.2 mm) = 20.8 mm

Thus, the final measured value is 20.8 mm, which falls within the specified range of 20.8 to 20.8 mm.