If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of the main scale is 0.5 mm, the Vernier constant of the travelling microscope is:
If 50 Vernier divisions are equal to 49 main scale divisions of a travelling microscope and one smallest reading of the main scale is 0.5 mm, the Vernier constant of the travelling microscope is:
- 0.01 mm
- 0.1 mm
- 0.1 cm
- 0.01 cm
The Correct Option is A
Approach Solution - 1
The Vernier constant (VC) is calculated as:
\[ \text{VC} = \text{Value of 1 MSD} - \text{Value of 1 VSD} \]
Given that 50 Vernier divisions correspond to 49 main scale divisions:
- The value of 1 MSD is 0.5 mm.
- Therefore, the value of 1 VSD is:
\[ \text{Value of 1 VSD} = \frac{49 \times 0.5 \text{ mm}}{50} = 0.49 \text{ mm} \]
Calculating the VC:
\[ \text{VC} = 0.5 \text{ mm} - 0.49 \text{ mm} = 0.01 \text{ mm} \]
Approach Solution -2
This problem requires us to calculate the Vernier constant (which is the same as the least count) of a travelling microscope, given the relationship between its main scale divisions and Vernier scale divisions.
Concept Used:
The Vernier constant (VC) or Least Count (LC) of a Vernier instrument is the smallest measurement that can be accurately made with the instrument. It is defined as the difference between the value of one main scale division (MSD) and one Vernier scale division (VSD).
\[ \text{Vernier Constant (VC)} = \text{Value of 1 MSD} - \text{Value of 1 VSD} \]To use this formula, we first need to find the value of one Vernier scale division (VSD) using the given relationship between the two scales.
Step-by-Step Solution:
Step 1: Identify the given information from the problem statement.
We are given:
- The value of the smallest division on the main scale, which is the value of one main scale division (1 MSD). \[ 1 \text{ MSD} = 0.5 \text{ mm} \]
- The relationship between the main scale and the Vernier scale: 50 divisions on the Vernier scale coincide with 49 divisions on the main scale. \[ 50 \text{ VSD} = 49 \text{ MSD} \]
Step 2: Calculate the value of one Vernier scale division (1 VSD).
Using the given relationship, we can express the value of 1 VSD in terms of MSD.
\[ 50 \text{ VSD} = 49 \text{ MSD} \]Dividing both sides by 50, we get:
\[ 1 \text{ VSD} = \frac{49}{50} \text{ MSD} \]Now, we substitute the given value of 1 MSD = 0.5 mm to find the value of 1 VSD in millimeters.
\[ 1 \text{ VSD} = \frac{49}{50} \times 0.5 \text{ mm} = 0.98 \times 0.5 \text{ mm} = 0.49 \text{ mm} \]Step 3: Calculate the Vernier constant (LC).
Using the formula for the Vernier constant:
\[ \text{LC} = 1 \text{ MSD} - 1 \text{ VSD} \]Substitute the values we have for 1 MSD and 1 VSD:
\[ \text{LC} = 0.5 \text{ mm} - 0.49 \text{ mm} \]Final Computation & Result:
Performing the final subtraction gives us the Vernier constant.
\[ \text{LC} = 0.01 \text{ mm} \]The Vernier constant of the travelling microscope is 0.01 mm.
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Concepts Used:
Units and Measurement
Unit:
A unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by the society and in terms of which other quantities of similar nature may be measured.
Measurement:
The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.
Read More: Fundamental and Derived Units of Measurement
System of Units:
- CGS system
- FPS system
- MKS system
- SI units
Types of Units:
Fundamental Units -
The units defined for the fundamental quantities are called fundamental units.
Derived Units -
The units of all other physical quantities which are derived from the fundamental units are called the derived units.