Question

One main scale division of a vernier caliper is equal to m units. If nth division of main scale coincides with (n + 1)th division of vernier scale,
the least count of the vernier caliper is:

• A. $\frac{n}{n+1}$
• B. $\frac{m}{n+1}$
• C. $\frac{1}{n+1}$
• D. $\frac{m}{n(n+1)}$

Answer 1

Answer: (B)

$\frac{m}{n+1}$

Answer 2

Step 1: Relationship between main scale and vernier scale Given that:

$n \, \text{MSD} = (n + 1) \, \text{VSD}.$

From this:

$1 \, \text{VSD} = \frac{n}{n + 1} \, \text{MSD}.$

Step 2: Least count formula The least count (L.C.) of a vernier caliper is given by:

$\text{L.C.} = 1 \, \text{MSD} - 1 \, \text{VSD}.$

Substitute $1 \, \text{VSD}$ from Step 1:

$\text{L.C.} = m - m \left( \frac{n}{n + 1} \right).$

Simplify:

$\text{L.C.} = m \left[ 1 - \frac{n}{n + 1} \right].$

$\text{L.C.} = m \left( \frac{n + 1 - n}{n + 1} \right).$

$\text{L.C.} = \frac{m}{n + 1}.$

Final Answer: $\frac{m}{n + 1}$.