Heat and Thermal ExpansionHard
Question
In a vernier calipers the main scale and the vernier scale are made up different materials. When the room temperature increases by ᐃToC 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 Nth main scale division and N + 2 MSD coincided with the 2nd VSD. Initially, 10 VSD coincided with 9 MSD. If coefficient of linear expansion of the main scale is α1 and that vernier scale is α2 then what is the value of α1 / α2 ? (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
Solution
Let 1 MSD = S & 1VSD = V
Given , 10V = 9S..... (i) Also given (N × S+2(S-V) = NS′ + 2(S′ - V′)
or (N + 2)(S′ - S) = 2(V′ - V)
or Sα1ᐃT =
(Vα1ᐃT)
or
Given , 10V = 9S..... (i) Also given (N × S+2(S-V) = NS′ + 2(S′ - V′)
or (N + 2)(S′ - S) = 2(V′ - V)
or Sα1ᐃT =
(Vα1ᐃT)or
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