The main scale of a vernier calliper has m divisions per centimetre. It is given that n divisions of the vernier scale coincide with (n-1) divisions of the main scale. While measuring the length of a cylinder, the zero of the vernier scale lies just after the k^ th mark of the main scale, and the p^ th division of the vernier scale coincides with a main scale mark. The measured length of the cylinder is

Step-by-step solution

The length of one main scale division is: 1 MSD = 1 m cm From the coincidence condition: n VSD = (n-1) MSD 1 VSD = n-1 n MSD The Least Count (LC) is: LC = 1 MSD - 1 VSD = 1 n MSD = 1 mn cm The total measured length is the sum of the Main Scale Reading (MSR) and the Vernier Scale Reading (VSR): MSR = k 1 MSD = k m cm VSR = p LC = p mn cm Total length = MSR + VSR = k m + p mn = kn+p mn cm Answer: kn+p mn cm