Question

There are two Vernier calipers both of which have $1\, cm$ divided into $10$ equal divisions on the main scale. The Vernier scale of one of the calipers $\left( C _{1}\right)$ has $10$ equal divisions that correspond to $9$ main scale divisions. The Vernier scale of the other caliper $\left( C _{2}\right)$ has $10$ equal divisions that correspond to $11$ main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in $cm$ ) by calipers $C _{1}$ and $C _{2}$, respectively, are

• A. 2.87 and 2.87
• B. 2.87 and 2.83
• C. 2.85 and 2.82
• D. 2.87 and 2.86

Answer 1

Answer: (B)

$MSD =\frac{1}{10} cm =0.1\, cm$
$VSD =\frac{9}{10} MSD \Rightarrow LC = MSD - VSD$
$LC =\frac{1}{10} MSD =0.01\, cm$
$C _{1}= 2.8+7( LC )$
$=2.8+7(0.01)$
$C _{1} \Rightarrow 2.87\, cm$
For $C _{2} 10\, VSD =11\, MSD$
$VSD =1.1( MSD )=1.1(0.1)=0.11\, cm$
$L C =|M S D-V S D|$
$=[1-(1.1)] MSD$
$=(-0.1)(0.1)$
$=-0.01\, cm$
Reading $=2.9+(7) LC$
$\Rightarrow 2.9+7(-0.01)$
$\Rightarrow 2.9-0.07$
Reading $=2.83\, cm$