Question

Which of the following is incorrect with respect to a standard vernier caliper?

• A. $L.C=\frac{1M.S.D}{N}$
• B. $L.C=1M.S.D-1V.S.D$
• C. 1M.S.D=1mm
• D. $L.C=\frac{1M.S.D}{1V.S.D}$

Answer 1

The correct option is B

$L.C=1M.S.D-1V.S.D$

Step 1: DEFINITION OF LEAST COUNT

It is the smallest measurement on any scale. The difference between one main scale division and the vernier scale division is also called as least count.

It is measured by the formula,

$Leastcount=\frac{smallestreadingofmainscaledivision}{totalnoofvernierscaledivisions}$

The least count of standard vernier calipers is 0.1 mm.

STEP 2: EXPLANATION FOR CORRECT OPTIONS

1. least count can be written as,$L.C=\frac{1M.S.D}{N}$
2. Here, the Vernier scale consists of N equally spaced divisions which have the same total length as (N - 1) main scale divisions.
3. so the total no of vernier divisions is represented by N
4. so option A is correct.
5. As per the definition, the difference between 1 M.S.D and 1 V.S.D is the least count
6. $L.C=1M.S.D-1V.S.D$
7. so option C is correct.
8. In the main scale, 1 M.S.D is equal to 1 mm
9. 1 M.S.D= 1 mm
10. so, option D is correct.

3. EXPLANATION FOR INCORRECT OPTIONS:

Option B is incorrect because the least does not equal the division of 1 M.S.D and 1 V.S.D it should be equal to the division of 1 M.S.D and the total no of vernier scale divisions.