Question

While measuring the length of a rod with Vernier callipers, given figures show the position of its scales. What is the length of the rod?

A) \[3.26cm\]
B) \[3.36cm\]
C) \[3.30cm\]
D) \[3.20cm\]

Answer 1

Hint: In order to find out the length of the rod, we first need to find the main scale reading and the vernier scale readings. This can be obtained by viewing the given figure. Then the least count of the vernier scale is calculated. The total reading is then obtained.

Complete step by step solution:
Vernier Callipers is an instrument that is used to measure small values with greater accuracy. The more accurate the measurement is indicates that it contains a negligible amount of errors.
The main components of the Vernier callipers are:
a) Main scale
b) Vernier scale
In order to measure a certain object, it is placed between the jaws of the Vernier calliper and the main scale and Vernier scale reading is obtained. From the obtained value of the Vernier constant we can obtain the Vernier constant of the scale.
Finally, by combining the main scale reading, Vernier scale reading and the least count depending upon the formula given below, we obtain the total reading of the scale.
The formula for total reading is:
\[TR = MSR + VSR\]
Where,
\[TR\] is the total reading of the rod.
\[MSR\] is the Main Scale Reading
\[VSR\] is the Vernier scale reading.
From the figure, we calculate the least count,
\[L.C. = \dfrac{{1MSD}}{{no.ofVSD}}\]

Here, as we can observe, there are \[10divisions\] in the main scale that reads one unit. So, \[1msd = 0.1cm\]
And there are \[10\] Vernier scale divisions, so:
\[LC = \dfrac{{0.1}}{{10}}cm = 0.01cm\]

As we can see the Vernier scale starts just after \[3.2\] reading in Main scale,
\[MSR = 3.2cm\]
Now, the previous formula is written as:
\[TR = MSR + (VSD \times LC)\]
\[VSD = \] Vernier scale division
From the figure, we observe
\[VSD = 6\]
Putting the values, we obtain:
\[TR = 3.2 + (6 \times 0.01)cm\]
Thus we obtain:
\[TR = 3.26cm\]
This is the required length of the rod.

Thus, the correct option is option (A).

Note: Vernier Scale Division, or VSD, is that division on the Vernier scale that completely coincides with any division on the main scale. From the figure, it is evident that \[VSD = 6\]. Vernier Callipers can only be used to measure small sized objects.