Final answer:
The least count of a vernier caliper where N main scale divisions coincide with N + 1 vernier scale divisions and each main scale division is 'a' units is calculated as a/N, which is the smallest increment the caliper can measure.
option b is the correct
Step-by-step explanation:
The question is asking how to determine the least count of a vernier caliper. The least count is the smallest measurement that can be obtained with a measuring tool and is based on the scale divisions of the instrument. For a vernier caliper where N divisions on the main scale coincide with (N + 1) divisions of the vernier scale, and each division on the main scale is 'a' units, the least count can be calculated.
One division on the vernier scale (VS) is slightly smaller than one division on the main scale (MS). Since N + 1 divisions on VS equal N divisions on MS, the difference in length between one MS division and one VS division is a/N. This difference represents the smallest increment that the vernier caliper can measure, which is the least count of the instrument.
Therefore, the least count of the instrument is option B, a/N. This is because one vernier scale division is 1/Nth of a main scale division less in size, and that small difference is how finely you can measure with this vernier caliper, giving you the least count.