Question

There are two Vernier calipers both of which have $1cm$ 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)

$MSD=\frac{1}{10}cm=0.1cm$
$VSD=\frac{9}{10}MSD\Rightarrow LC=MSD-VSD$
$LC=\frac{1}{10}MSD=0.01cm$
$C_1=2.8+7(LC)$
$=2.8+7(0.01)$
$C_1\Rightarrow 2.87cm$
For $C_{2}10VSD=11MSD$
$VSD=1.1(MSD)=1.1(0.1)=0.11cm$
$LC=|MSD-VSD|$
$=[1-(1.1)]MSD$
$=(-0.1)(0.1)$
$=-0.01cm$
Reading $=2.9+(7)LC$
$\Rightarrow 2.9+7(-0.01)$
$\Rightarrow 2.9-0.07$
Reading $=2.83cm$