10 divisions of a Vernier scale are equal to 11 divisions of a main scale of each 0.1 mm. What is the least count of the Vernier scale?

📝 Detailed Explanation: Understanding the Vernier Scale

The least count of a measuring instrument is the smallest and most accurate value that can be measured by it. A Vernier scale is a secondary scale that allows for more precise readings than a main scale alone. The key to finding its least count is understanding the relationship between the main scale divisions (MSD) and the Vernier scale divisions (VSD).

This specific problem describes a retrograde Vernier scale, where the divisions on the Vernier scale are slightly larger than the divisions on the main scale.

⚙️ Step-by-Step Calculation

The fundamental principle is that the least count is the difference between the value of one main scale division and one Vernier scale division.

1. Identify the Given Information:
   • Value of 1 Main Scale Division (MSD) = 0.1 mm
   • The relationship given is: 10 VSD = 11 MSD
2. Calculate the Value of 1 Vernier Scale Division (VSD):

   We can find the value of one VSD using the relationship provided.

   If 10 VSD = 11 MSD

   Then, 1 VSD = (11 / 10) MSD

   1 VSD = 1.1 × (Value of 1 MSD) = 1.1 × 0.1 mm = 0.11 mm

3. Calculate the Least Count (LC):

   The least count is the absolute difference between one VSD and one MSD.

   LC = | Value of 1 VSD - Value of 1 MSD |

   LC = | 0.11 mm - 0.1 mm |

   LC = 0.01 mm

💡 Key Concepts for Students

• Least Count (LC): The smallest measurement an instrument can accurately make. For a Vernier scale, it's the difference in size between a main scale division and a vernier scale division.
• Direct Vernier: The more common type, where 'n' divisions on the Vernier scale are equal to 'n-1' divisions on the main scale (e.g., 10 VSD = 9 MSD). Here, VSD < MSD.
• Retrograde Vernier: The type in this question, where 'n' divisions on the Vernier scale are equal to 'n+1' divisions on the main scale (e.g., 10 VSD = 11 MSD). Here, VSD > MSD.