Question 311: Units , Dimensions and Error Analysis

Question

If n
th
divisions of the main scale coincide with (n+1)
th
divisions
of vernier scale. Given one main scale division is equal to 'a' units. Find the
least count of the vernier.

Accepted Answer

We know that (n + 1) divisions on the vernier scale = n division on the main scale
Therefore,
1 division on the vernier scale = $$\left( {{n \over {n + 1}}} \right)$$ divisions on the main scale = $$\left( {{n \over {n + 1}}} \right)a$$ units
Therefore, the least count (LC) of the vernier caliper is
$$1(MSD) - 1(VSD) = a - \left( {{n \over {n + 1}}} \right)a = {a \over {n + 1}}$$

Units , Dimensions and Error Analysis

If n th divisions of the main scale coincide with (n+1) th divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.

Integer / Numeric Answer Type