The smallest division on main scale of a vernier caplliers is `1 mm and 10` vernier divisions coincide with `9` main scale divisions. While measuring the length of a line, the zero mark of the vernier scale lies between `10.2 cm and 10.3 cm` and the third division of vernier scale coincides with a main scale division.
(a) Determine the least count of the callopers.
(b) Find the length of the line.

Explanation

To solve the problem step by step, we will break it down into two parts: (a) determining the least count of the vernier calipers and (b) finding the length of the line measured.

### Step-by-Step Solution

#### Part (a): Determine the Least Count of the Calipers

1. **Identify the smallest division of the main scale (MSD)**:
- The smallest division on the main scale is given as **1 mm**.
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