Question

The least count of the main scale of a vernier callipers is $1$mm. Its vernier scale is divided into $10$ divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the $7th$ division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between $3.1$ cm and $3.2$ cm and $4th$ VSD coincides with a main scale division. The length of the cylinder is: (VSD is vernier scale division)

• A. $3.21cm$
• B. $3.07cm$
• C. $2.99cm$
• D. $3.2cm$

Answer 1

The correct option is B

$3.07cm$

Solution:

Step 1: Given data:

The scale division (MSD)$=1mm$

$10$ vernier scale divisions $=9$main scale divisions.

One vernier scale divisions (VSD)$=\frac{9}{10}MSD=0.9mm$.

Step 2: Formula used:

The vernier constant or least count of instrument is,

$LC=1MSD-1VSD$, where $LC=$least count

Step 3:Evaluate the values in the formula:

$$\begin{gathered} LC=1MSD-\frac{9}{10}MSD \\ LC=\frac{10-9}{10}MSD \\ LC=\frac{1}{10}MSD \\ LC=0.1mm \end{gathered}$$

Note that the zero of vernier scale lies to the right of the main scale, so the error is positive.

Zero error

$$\begin{gathered} =7\times LC \\ =7\times 0.01cm \\ =0.07cm \end{gathered}$$

Step 4: Formula used and evaluate the value in the formula,

Observed value =$MSR+VSR\times LC-Zeroerror$

Know that main scale reading $=3.1cm$

Vernier scale reading$=4division$

Therefore the observed value

$$\begin{gathered} =3.1+4\times 0.01-0.07 \\ =3.14cm-0.07cm \\ =3.07cm \end{gathered}$$

Therefore the length of the cylinder is$3.07cm$.

Hence, the correct option is C.