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# 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 $x$ .

Last updated date: 17th Sep 2024
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Hint: 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 $1$.

${\text{Least Count = }}\dfrac{{{\text{Least count of main scale}}}}{{{\text{Number of divisions on Vernier scale}}}}$
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 $0.01cm$.