Question

State whether the following statements are true or false.

In a vernier caliper, if $1\mathrm{M}.\mathrm{S}.\mathrm{D}.=0.1\mathrm{cm}$ and the least count is $0.1\mathrm{mm}$, then $1\mathrm{V}.\mathrm{S}.\mathrm{D}.=0.9\mathrm{mm}$

• A. True
• B. False

Answer 1

The correct option is B False

Step1: Given data:

$1\mathrm{MSD}$of the Vernier caliper$=0.1\mathrm{cm}$

$$\begin{gathered} =\frac{1}{10}\mathrm{cm} \\ =\frac{1}{10}10\mathrm{mm} \\ =1\mathrm{mm} \end{gathered}$$

Step 2: To calculate VSD on applying the least count formula of a vernier caliper,

$\mathrm{Least}\mathrm{count}=0.1\mathrm{mm}$

$$\begin{gathered} \because \mathrm{L}.\mathrm{C}.=\frac{\mathrm{MSD}\left(\mathrm{mm}\right)}{\mathrm{VSD}\left(\mathrm{mm}\right)} \\ 0.1mm=\frac{1\mathrm{mm}}{\mathrm{VSD}\left(\mathrm{mm}\right)} \\ \therefore \mathrm{VSD}\left(\mathrm{N}\right)=\frac{1}{0.1} \\ =10\mathrm{division}. \end{gathered}$$

$\because Weknow;\left(N\right)V.S.D.=(N-1)M.S.D.$

$$\begin{gathered} 10\mathrm{V}.\mathrm{S}.\mathrm{D}.=(10-1)\mathrm{M}.\mathrm{S}.\mathrm{D}. \\ =9\mathrm{MSD} \\ \because 1\mathrm{M}.\mathrm{S}.\mathrm{D}=1\mathrm{mm}.....\left(given\right) \\ 9\mathrm{M}.\mathrm{S}.\mathrm{D}=9\mathrm{mm} \\ =0.9\mathrm{cm} \\ Thus;10V.S.D.=0.9cm \end{gathered}$$

Hence, The given statement is false.