A height gauge (an instrument used to measure accurately the height of the part of machinery) is to be constructed using a main scale marked in centimeters and millimetres.
(i) What is the minimum length of the vernier scale if the required least count is 0.001 cm?
(ii) what least count can be achieved if the number of vernier scale divisions cannot be more than 50?

Explanation

(i) What is 1 M.S.D . For given height guage?
The formula for L.C. of an appartus
= 1 M.S.D. - 1 V.S.D. = `(1.M.S.D.)/(N)`
What is the value of L.C. of given instrument?
Then, is the number of divisions present on vernier scale?
Then, the value of 1 V.S.D. = 1 M.S.D. - L.C.
If the value of N is 50, and 1 M.S.D. = 1 mm
then what is the value of L.C.?
(ii) Minimum length of the vernier scale = 9.9 cm
(iii) Least count = 0.02 mm