There are two Vernier calipers both of which have `1cm` divided into `10` equal divisions on the main scale. The vernier scale of the calipers `( c_(1))` has `10` equal divisions that correspond to `9` main scale divisions. The Vernier scale of the other calipers `( C_(2))` has `10` equal divisions tgat correspond to `11` main scale divisions. the reading of the two calipers are shown in the figure. the measured values (in cm) by calipers `C_(1) and C_(2)` respectively, are

Options

A. `2.87" and "2.86`
B. `2.85" and "2.82`
C. `2.87" and "2.87`
D. `2.87" and "2.83`

Answer

D

Explanation

`C_(1)` : 1 Main scale division MSD = 0.1 cm
1 vernier scale division VSD `=(0.9)/(10)=0.09 cm`
Least count `LC = 1 MSD - 1VSD = 0.1 -0.09= 0.01cm`
Main scale reading MSR = 2.8 cm
Number of vernier division matching main scale division n= 7
Reading `R_(1)= MSR +n xx LC = 2.8+7xx0.01= 2.87 cm`
`C_(2)` : 1 Main scale division MSD = 0.1 cm
1 vernier scale division VSD `=(1.1)/(10)=0.11 cm`
Least count `LC = 1 VSD - 1MSD = 0.11 -0.1 = 0.01cm`
Main scale reading MSR = 2.8 cm
Here we should note that size of vernier scale division is bigger than main scale division, hence number of vernier division matching main scale division will be counted form back. In given figure we can see that 7th vernier scale division is matching so we shall consider 10-7 = 3rd.
Number of vernier division matching main scale division (n)= 3
Reading `R_(2)= MSR +n xx LC = 2.8+3 xx0.01= 2.83 cm`
Nothing down `R_(1)" and "R_(2)` we can see that option d is correct.