A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is

The correct option is 0.2mm.

To find the least count of the Vernier calipers, we use the standard formula for the least count (LC):

$\text{Least Count (LC)}=1\text{MSD}-1\text{VSD}$

where:
• MSD is the value of one Main Scale Division.
• VSD is the value of one Vernier Scale Division.

From the given data:
• The main scale has 1 mm marks, so:
$1\text{MSD}=1\text{mm}$

• 20 Vernier scale divisions (VSD) match with 16 main scale divisions (MSD):
$20\text{VSD}=16\text{MSD}$

• Therefore, the value of one Vernier scale division (1 VSD) is:
$1\text{VSD}=\frac{16}{20}\text{MSD}=0.8\text{MSD}$

Since $1\text{MSD}=1\text{mm}$, we have:
$1\text{VSD}=0.8\times 1\text{mm}=0.8\text{mm}$

Now, calculate the least count (LC):
$\text{LC}=1\text{MSD}-1\text{VSD}$
$\text{LC}=1\text{mm}-0.8\text{mm}=0.2\text{mm}$

Thus, the least count of this Vernier calipers is 0.2 mm.