Determine Zero Error in Vernier Caliper Measurement

To determine the zero error of the Vernier caliper, we calculate the Least Count ($\text{LC}$) and use the position of the Vernier scale's zero mark relative to the main scale's zero mark.

1. Least Count ($\text{LC}$) Calculation: Given:

   • Value of $1\text{ Main Scale Division (MSD)} = 1\text{ mm} = 0.1\text{ cm}$
   • Total number of Vernier scale divisions ($N$) = $10$

   The Least Count ($\text{LC}$) of the Vernier caliper is given by: $\text{LC} = \frac{1\text{ MSD}}{N} = \frac{1\text{ mm}}{10} = 0.1\text{ mm} = 0.01\text{ cm}$

2. Sign of the Zero Error: When both jaws touch each other, the zero of the Vernier scale lies to the right of the zero of the main scale. Hence, the zero error is positive.

3. Magnitude of the Zero Error: The positive zero error is calculated using the coinciding division of the Vernier scale: $\text{Zero Error} = + (\text{Coinciding Vernier Division}) \times \text{LC}$ $\text{Zero Error} = + (7 \times 0.01\text{ cm}) = + 0.07\text{ cm}$

Therefore, the Vernier caliper has a $0.07\text{ cm}$ positive zero error.

Correct Option: C