Question

Describe in steps, how would you use a vernier callipers to measure the length of a small rod?

Answer 1

Fig. illustrates the use of a vernier scale. The two scales (main scale and vernier scale) are so made that when the movable vernier scale touches the fixed end, its zero mark coincides with the zero mark of the main scale. The rod whose length is to be measured is placed along the main scale, and the vernier scale is moved so as to hold the rod between the fixed end and the movable vernier scale. In this position, the zero mark of the vernier scale is ahead of the 1.2 cm mark on the main scale. Thus, the actual length of the rod = 1.2 cm + the length ab (i.e., the length between the 1.2 cm mark on the main scale and the 0 mark on the vernier scale). The length ab cannot be measured by the main scale as its value is less than one division marked on the main scale.

To measure the length of ab, we first find the lowest count on the vernier scale. It is `0.1/10` cm = 0.01 cm. Then we note that p^th division of the vernier scale which coincides (or which is in line) with any division of the main scale. The product of this number of vernier divisions, p, with the least count, gives the length ab. This is called the vernier reading. Thus 

length ab = vernier reading = p × least count, 

and Total reading = main scale reading + vernier reading

In the given figure, the the main scale reading is 1.2 cm, and 4^th division of vernier scale coincides with a main scale division, so the length ab (or vernier reading) is 4 × 0.01 cm = 0.04 cm.

Hence, the length of the rod is 1.2 + 0.04 = 1.24 cm.