Vernier calipers are precision instruments used for measuring internal and external dimensions with high accuracy. The instrument consists of a main scale and a Vernier scale. The main scale typically has millimeter markings, while the Vernier scale provides additional precision by subdividing the main scale divisions into finer intervals.
| Property | Description |
| Measurement Tool | Vernier Caliper |
| Main Scale | 1 mm divisions |
| Vernier Scale | 20 equal divisions matching 16 main scale divisions |
| Unknown | Least Count (LC) of the vernier caliper |
Explanation:
The least count (LC) of the Vernier calipers is the smallest distance that it can measure and is determined by the difference in length between one main scale division and one Vernier scale division. To find the LC, the value of one main scale division is divided by the number of Vernier scale divisions.
These relationships express the fundamental units of mass, length, and time in a system where the speed of light, the gravitational constant, and Planck’s constant are the base units.
Calculation steps:
- Identify the Value of One Main Scale Division: Each main scale division is given as 1 mm.
- Total Length of 16 Main Scale Divisions: Since the Vernier scale’s 20 divisions are equal in length to 16 divisions on the main scale, the total length that these 16 divisions cover is
mm, which equals 16 mm. - Length of One Vernier Scale Division: To find out the length that one division on the Vernier scale represents, divide the total length covered by the 16 main scale divisions by the number of Vernier scale divisions. This is calculated as ( \frac{16 \text{ mm}}{20} ).
- Calculate the Least Count: The least count of the Vernier calipers is the difference between the length of one main scale division and one Vernier scale division. Therefore, it’s
. - Perform the Subtraction: Subtract the length of one Vernier scale division from the length of one main scale division to find the least count:
![\[ LC = 1 \text{ mm} - \frac{16 \text{ mm}}{20} \]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-2a5454cc86e7315d421fa41d62eb3033_l3.png "Rendered by QuickLaTeX.com")
![\[ LC = 1 \text{ mm} - 0.8 \text{ mm} \]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-67b4afd17108b8b9321e5753ec431e2f_l3.png "Rendered by QuickLaTeX.com")
![\[ LC = 0.2 \text{ mm} \]](https://physicsqanda.com/wp-content/ql-cache/quicklatex.com-a07311ed8387a373fbc9a355ed8a1eef_l3.png "Rendered by QuickLaTeX.com")
So the least count of the Vernier calipers, which is the minimum measurement it can accurately indicate, is found to be 
.
. If linear charge density is 
, then calculate the speed of an electron. (
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