A student uses a standard Vernier calliper ( 1 main scale division...

The least count (LC) of the standard Vernier calliper is:

$\text{LC} = 1 \text{ mm} - 0.9 \text{ mm} = 0.1 \text{ mm} = 0.01 \text{ cm}$

The observed reading during the measurement is:

$\text{Observed reading} = \text{MSR} + (\text{VSR} \times \text{LC}) = 3.1 \text{ cm} + (7 \times 0.01 \text{ cm}) = 3.17 \text{ cm}$

The relationship between actual thickness, observed reading, and zero error is:

$\text{Actual reading} = \text{Observed reading} - \text{Zero error}$

$3.20 \text{ cm} = 3.17 \text{ cm} - \text{Zero error}$

$\text{Zero error} = 3.17 \text{ cm} - 3.20 \text{ cm} = -0.03 \text{ cm}$

For a negative zero error, the zero of the Vernier scale is to the left of the main scale zero. The magnitude of the error is given by:

$\text{Zero error} = -(N - n) \times \text{LC}$

where $N$ is the total number of Vernier divisions ($10$)$and n$ is the coinciding division.

$-0.03 \text{ cm} = -(10 - n) \times 0.01 \text{ cm}$

$10 - n = 3 \implies n = 7$

Thus, the $7^{th}$ Vernier division coincides when the jaws are in contact.

Answer: $7^{th}$