Question

The length of an iron rod measured by Vernier calipers is $3.06cm$. Choose the value of the number of divisions on the Vernier scale if the main scale division on it is $0.2cm$ and the Vernier scale reading is $6$.

• A. $10$
• B. $30$
• C. $20$
• D. 40

Answer 1

The correct option is C

$20$

Step 1: Given the value and formula used

$(M.S.D)$ Main Scale Division$=0.2cm$
$(V.S.D)$Vernier Scale Division$=6cm$
$\left(MSR\right)$ Main Scale Reading $=3cm$

$(L.C)$stands for least count$=3.06$ $Length=3.06cm$

Formula used:
$Length=M.S.R+(V.C.D)\times L.C$

$L.C=\frac{1M.S.D}{NumberofV.S.D}$

Step 2: Calculation of Number of scale division (N)

On putting the given value in the formula
$3.06=MSR+V.CD\times L.C$

$$\begin{gathered} 3.06=3+6\times \frac{0.2}{N} \\ 0.06=6\times \frac{0.2}{N} \\ N=20 \end{gathered}$$

Hence correct option is (b).