In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4^ th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 ~mm then how many main scale divisions are there in 1 ~cm ?

Step-by-step solution

aligned & 50 VSD =49 MSD & 1 VSD = 49 50 MSD & LC =1 MSD -1 VSD & LC =1 MSD 49 50 MSD = MSD 50 . . . . . .(1) & Now, | zero error |=| 0-4( ~L . C ) | & 0.04=|-4( ~L . C )| L . C =0.01 ~mm & 0 . 0 4 =|- 4 ( L . C )| L . C . . .(2) & = 0 . 0 1 mm aligned Using (1) and (2) aligned & M S D 50 =0.01 & M S D=0.5 ~mm & M S D= 1 ~cm ~N & ~N = 1 ~cm 0.5 ~mm = 100 ~mm 5 ~mm & ~N =20 aligned