JEE Class main Answered
In a vernier calipers the main scale and the vernier scale are made up of different materials. When the room temperature increases by ?ToC, it is found that 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 the 2nd vsd. Initially, 10 vsd coincided with 9 msd. If coefficient of linear expansion of the main scale is ?1? and that of the vernier scale is ?2? then what is the value of ?1?/?2?? (Ignore the expansion of the rod on
Asked by shailuupd | 21 Apr, 2022, 21:24: PM
Expert Answer
Initially 10 vernier scal divisions ( vsd ) equals 9 main scale divisions ( msd ) .
Hence , 1 vsd = (9/10) msd = 0.9 msd
After thermal expansion , vernier instrument gives same reading .hence expanded 1 vsd equals 0.9 times of expanded msd
if thermal expansion coefficient of main scale is α1 and vernier is α2 , then
( vsd ) α1 ΔT = 0.9 ( msd ) α2 ΔT
α1 ΔT = α2 ΔT
α1 / α2 = 1
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