Given below are two statements:
Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division.
Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.
In light of the above statements, choose the correct answer from the options given below.
Show Hint
- Both Statement I and Statement II are false.
- Statement I is true but Statement II is false.
- Both Statement I and Statement II are true.
- Statement I is false but Statement II is true.
The Correct Option is B
Approach Solution - 1
To solve the given problem, let's analyze each statement independently:
Statement I: In a vernier calipers, one vernier scale division is always smaller than one main scale division.
The vernier caliper is a precision instrument used to measure lengths. It consists of a main scale and a sliding vernier scale. Typically, each vernier scale division is slightly smaller than a main scale division. This is a fundamental design principle of a vernier caliper, enabling it to measure smaller increments accurately by using the difference between these scales. Thus, Statement I is true.
Statement II: The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.
The vernier constant (also called the least count) is defined as the difference between one main scale division and one vernier scale division. Mathematically, it is given by:
Vernier Constant = Length of one main scale division - Length of one vernier scale division.
The statement suggests it is calculated by multiplying a main scale division by the number of vernier scale divisions, which is incorrect. The vernier constant is determined by the small difference between these divisions, not multiplication. Therefore, Statement II is false.
Based on this analysis, the correct answer is: Statement I is true but Statement II is false.
Approach Solution -2
Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division.
Statement II: The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions.
Analysis:
In a vernier callipers, one vernier scale division (VSD) is indeed smaller than one main scale division (MSD). This is why the vernier gives more precise readings — hence, Statement I is true.
The vernier constant (VC) is defined as the difference between one main scale division and one vernier scale division, that is,
$$ VC = 1 \, \text{MSD} - 1 \, \text{VSD} $$ and not the product of one main scale division and the number of vernier scale divisions. Hence, Statement II is false.
Correct Answer: Option 2 — Statement I is true but Statement II is false.
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