In a vernier callipers the main scale and the vernier scale are made up different materials. When the room temperature increases by `DeltaT^(@)C`, it is found the reading of the instrument remains the same. Earlier it was observed that the front edge of the wooden rod placed for measurement crossed the `N^(th)` main scale division and N + 2 MSD coincided with the 2nd VSD. Initially, 10 VSD coincided with 9MSD. If coefficient of linear expansion of the main scale is `alpha_(1)` and that of the vernier scale is `alpha_(2)` then what is the value of `alpha_(1)//alpha_(2)` ? (Ignore the expansion of the rod on heating)

Options

A. `1.8//N`
B. `1.8//(N+3.8)`
C. `1.8//(N-2)`
D. `1.8//N+2`

Answer

B

Explanation

Let 1 MSF = S & 1 VSD = V
Given, `10 V=9S or S= V`….(i)
Also given `(NxxS(+2(S-V)=NS'+2(S'-V')`
or `(N+2)(S'-S)=2(V'-V)`
or `Salpha_(1)DeltaT=(2)/(N+2)(V alpha_(2)DeltaT)`
or `(alpha_(1))/(alpha_(2))=((2)/(N+2))xx(V)/(S)=(2)/(N+2)xx(9)/(10)=(1.8)/(N+2)`