Question

If the zero of the vernier lies between $3.2$ and $3.3$ cm on the main scale, the MSR is $32 \times {10^{ - x}}$ . Find the value of $x$ .

Answer 1

In vernier calipers, the zero of the vernier scale is to the left of the zero of the main scale when the movable jaw is in contact with the fixed jaw. If the zero of the vernier does not exactly match with any main scale, the left side value means the minimum value will give the main scale reading (MSR).

Complete step by step solution:
Here since the zero of the vernier does not exactly match with any main scale, the left side value means the minimum value will give the main scale reading (MSR). Thus the left side value( minimum value) in this case is $3.2$ (out of $3.2$ and $3.3$).
Thus MSR = 3.2cm$$$$ = 32 \times {10^{ - 1}}cm
But Given MSR in question $= 32 \times {10^{ - x}}cm$
By comparing the value of main scale reading (MSR) and the evaluated main scale reading (MSR),

The value of $x$ is found to be $1$.

Additional Information:
We can also find the least count of the vernier caliper.
The least count as the name suggests is the finest measurement you can take with the help of that Vernier calipers. It is measured by dividing the least count of the main scale by the total number of divisions on the Vernier scale. The Least Count (LC) of the Vernier scale is given as
${\text{Least Count = }}\dfrac{{{\text{Least count of main scale}}}}{{{\text{Number of divisions on Vernier scale}}}}$
Least count of the main scale: The main scale is calibrated in millimeters. To get the least count of the main scale, count the number of divisions on the main scale in one cm of it. Divide $1cm$ into that much number of divisions; the value obtained is the least count of the main scale in cm. For example, if there are $10$ divisions in one centimeter of the main scale its least count $= \dfrac{1}{{10}} = 0.1cm$
Number of divisions on the Vernier scale: In most Vernier calipers, the Vernier scale has $10$ divisions. Count the number of divisions on the Vernier scale. Use a magnifying glass if necessary.
For most Vernier calipers least count of main scale $= 0.01cm$ and number of divisions on Vernier scale $= 10$ divisions.
Thus, Least Count of Vernier calipers $= \dfrac{{0.1}}{{10}}cm$
Least Count of Vernier calipers$= 0.01cm$
Since the least count of the Vernier caliper is $0.01cm$, it can be said that when measuring with the help of this Vernier caliper, you can get an accuracy of $0.01cm$.

Note: We can also find the zero error of this vernier caliper. Zero error is defined as the condition where a measuring instrument registers a reading when there should not be any reading. In the case of vernier calipers, when the zeroth division on the vernier scale does not coincide with the zeroth division on the main scale, the vernier calipers have zero error. It can be either positive or negative.