Question

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

• A. \(\frac{1}{2}\)
• B. \(\frac{10}{11}\)
• C. \(\frac{50}{11}\)
• D. \(\frac{5}{11}\)

Answer 1

The Correct Option is D

Given:

\[ 10 \, \text{MSD} = 11 \, \text{VSD} \]

1 VSD (Vernier Scale Division) is equivalent to:

\[ 1 \, \text{VSD} = \frac{10}{11} \, \text{MSD} \]

The least count (LC) of the Vernier caliper is given by:

\[ LC = 1 \, \text{MSD} - 1 \, \text{VSD} \]

Substituting the values:

\[ LC = 1 \, \text{MSD} - \frac{10}{11} \, \text{MSD} = \frac{1}{11} \, \text{MSD} \]

Given that 1 MSD corresponds to 5 units:

\[ LC = \frac{5 \, \text{units}}{11} \]