Question

In a Vernier caliper, $15$ Vernier scale divisions correspond to $14$ main scale division, and one main scale division is equal to $1.5\mathrm{mm}.$ An object held between the external jaws of the given Vernier calipers. If the zeroth division of the Vernier scale is to the left of the ${20}^{\mathrm{th}}$ division of the main scale, find the measurement of the object; if the 14th division of the Vernier scale coincides with the main division.

Answer 1

Step 1: Given data

One main scale division $\left(\mathrm{MSD}\right)=1.5\mathrm{mm}$

No. of Vernier scale division (V.S.D.) $=15$

Vernier coincidence division, $\mathrm{V}.\mathrm{C}.\mathrm{D}.=14$

Step 2: Formula for L.C

If the zeroth division of the Vernier scale is to the left of the ${20}^{\mathrm{th}}$ division of the main scale, i.e., 19.

$\therefore Mainscalereading\left(MSR\right)=19\times 1.5\mathrm{mm}=28.5\mathrm{mm}$

Calculate the least count of the given Vernier scale.

$$\begin{gathered} \because Leastcount\left(LC\right)=\frac{1\mathrm{MSD}}{\mathrm{N}} \\ =\frac{1.5}{15} \\ =0.1\mathrm{mm} \end{gathered}$$

Step 3: On applying the length measurement formula of Vernier caliper measurement

Length (L) $=\mathrm{M}.\mathrm{S}.\mathrm{R}.+\mathrm{V}.\mathrm{C}.D\times \mathrm{L}.\mathrm{C}.$

$=28.5+14\times 0.1$

$=28.5+1.4$

$=29.9mm$

$=2.99\mathrm{cm}$

Hence, the measurement of the object is $2.99\mathrm{cm}$ or $29.9mm$