Question

A traveling microscope has 20 divisions per cm on the main scale while its vernier scale has a total of 50 divisions, and 25 vernier scale divisions are equal to 24 main scale divisions. What is the least count?

(a) 0.001 cm
(b) 0.002 cm
(c) 0.004 cm
(d) 0.005 cm

Answer 1

The least count of the traveling microscope is calculated by finding the difference between one main scale division and one vernier scale division. After performing the calculations, the least count is found to be 0.002 cm, which corresponds to answer option (b).

Step-by-step explanation:

You've asked how to find the least count of a traveling microscope given that it has 20 divisions per cm on the main scale, and its vernier scale has 50 divisions, with 25 vernier scale divisions being equal to 24 main scale divisions. To calculate the least count, we follow these steps:

1. First, determine the value of one main scale division (MSD). Since there are 20 divisions per cm, one division is 1/20 cm or 0.05 cm.
2. Next, find out the value of one vernier scale division (VSD). As 25 VSDs are equal to 24 MSDs, and one MSD is 0.05 cm, then 25 VSDs equal 24 x 0.05 cm. Therefore, one VSD equals (24 x 0.05 cm) / 25.
3. Finally, the least count (LC), which is the minimum distance that can be measured by the instrument, is the difference between one MSD and one VSD. So, LC is 0.05 cm minus the value of one VSD calculated in step 2.

After calculating, we find that the least count is 0.002 cm. So, the correct answer is (b) 0.002 cm.