The vernier caliper is a measuring instrument that allows for precise measurements of small objects. It consists of a main scale and a vernier scale. The main scale is marked in millimeters or inches, while the vernier scale provides additional decimal readings.
In the given information, it is stated that 10 divisions on the vernier scale correspond to 9 divisions on the main scale. This means that the distance between two consecutive vernier divisions is smaller than the distance between two consecutive main scale divisions.
To prove that the vernier caliper can be used to make readings to 1/10 of a main scale division, let's consider an example. Suppose we have a main scale division of 1 mm. Since 10 vernier divisions correspond to 9 main scale divisions, the distance between two consecutive vernier divisions would be (1 mm / 10) * 9 = 0.9 mm.
Now, let's say we want to measure an object and the vernier scale aligns with a main scale division at 4.7 mm. We can see that the vernier scale has moved beyond the 4.6 mm mark but has not reached the 4.7 mm mark. By observing the vernier scale, we can determine which vernier division aligns exactly with a main scale division. In this case, let's say the vernier division aligning with the main scale is the 3rd division.
Since each vernier division represents a difference of 0.9 mm from the previous main scale division, we can calculate the measurement as follows:
Main scale reading: 4.6 mm
Vernier scale reading: 3 divisions * 0.9 mm/division = 2.7 mm
Adding the main scale reading and the vernier scale reading gives us the total measurement:
Total measurement: 4.6 mm + 2.7 mm = 7.3 mm
By using the vernier scale, we were able to measure the object to a precision of 1/10 of a main scale division, as the vernier scale allowed us to read the measurement beyond the 4.6 mm mark on the main scale.
In summary, the vernier caliper can be used to make readings to 1/10 of a main scale division by utilizing the additional decimal readings provided by the vernier scale.