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Chapter 21: Problem 2771

N divisions on the main scale of a vernier calipers coin sides with \((\mathrm{N}+1)\) divisions on the vernier scale. If each division on the main scale is of a units, the least of count of instrument is................ (A) \(\\{\mathrm{a} /(\mathrm{N}+1)\\}\) (B) \(\\{\mathrm{a} /(\mathrm{N}-1)\\}\) (C) \(\\{(N+1) / a\\}\) (D) \(\\{(N-1) / a\\}\)

Short Answer

Expert verified
The least count of the instrument is (A) \(\\{\mathrm{a} /(\mathrm{N}+1)\\}\).

Step by step solution

01

Finding the value of one division on the vernier scale

The least count can be calculated as the difference between one main scale reading and one vernier scale reading. From the given information, we know that N divisions on the main scale coincide with (N+1) divisions on the vernier scale. Let's denote the value of one division on the vernier scale as "b" units. Therefore: \(Nb = (N+1)b\)
02

Solve for the value of b

Now, in order to find the value of one vernier scale reading, we will solve for b in the above equation. Divide both sides of the equation by N(N+1): \(\frac{Nb}{N(N+1)} = \frac{(N+1)b}{N(N+1)}\) This simplifies to: \(\frac{b}{N+1} = a\) Now, solve for b: \(b = a(N+1)\)
03

Calculate the least count

The least count of the instrument is the difference between one main scale reading (a) and one vernier scale reading (b). Least count = \(|a - b|\) Substitute the value of b from step 2: Least count = \(|a - a(N+1)|\) Least count = \(|a(1 - (N+1))|\) Least count = \(|a(N+1 - N - 1)|\) Least count = \(a / (\mathrm{N} + 1)\) Comparing our result with the given options, we find that the correct option is: (A) \(\\{\mathrm{a} /(\mathrm{N}+1)\\}\)

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Most popular questions from this chapter

When the zero mark on the vernier scale lies towards the right side of the zero mark of the main scale, when the jaws are in contact, then what will be the zero error? (A) zero correction in positive (B) zero correction is negative (C) zero error in positive (D) zero error does not exist

In an unusual vernier, 9 vernier scale divisions coincide with 8 main scale division, then what is the least count of the vernier? (A) \((8 / 9) \mathrm{mm}\) (B) \((1 / 9) \mathrm{mm}\) (C) \((1 / 17) \mathrm{mm}\) (D) \((1 / 8) \mathrm{mm}\)

If observed reading is OR, corrected reading is CR, zero error in \(\mathrm{ZE}\) and zero correction in \(\mathrm{ZC}\), then what will be the possibility? (A) \(\mathrm{CR}=\mathrm{OR}+\mathrm{ZC}\) and \(\mathrm{ZE}=\mathrm{CR}-\mathrm{OR}\) (B) \(\mathrm{CR}=\mathrm{OR}+\mathrm{ZE}\) and \(\mathrm{ZC}=\mathrm{CR}-\mathrm{OR}\) (C) \(\mathrm{CR}=\mathrm{OR}-\mathrm{ZC}\) and \(\mathrm{ZE}=\mathrm{OR}-\mathrm{CR}\) (D) \(\mathrm{CR}=\mathrm{OR}-\mathrm{ZE}\) and \(\mathrm{ZC}=\mathrm{CR}-\mathrm{OR}\)

What is the least count of commonly available vernier? (A) \(0.01 \mathrm{~cm}\) (B) \(0.001 \mathrm{~cm}\) (C) \(0.0001 \mathrm{~cm}\) (D) \(0.1 \mathrm{~cm}\)

What is the least count of the vernier calipers? (A) Smallest division on the vernier scale. (B) difference of the smallest division on the main scale and the smallest division on the vernier scale. (C) sum of the smallest division on the main scale and the smallest division on the vernier scale. (D) smallest division on the main scale.
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