Question

The zero line of the Vernier scale lies between divisions 20 and 21 of the main scale. The 4^th Vernier scale division exactly coincides with a main scale division. The 5 divisions of the Vernier scale are equal to 4 divisions of the main scale. If one main scale division is 1 mm, the measured value (in mm) is ........... (Rounded off to one decimal place)

Hint:

In Vernier scale measurements, the main scale reading is combined with the Vernier scale reading to give the final measurement.

Answer 1

From the problem, we know:
- The 5 divisions of the Vernier scale are equal to 4 divisions of the main scale.
- One main scale division (MSD) is 1 mm.
- The 4superscript{th} Vernier scale division coincides with a main scale division.
First, calculate the length of one Vernier scale division:
\[ {Length of one Vernier scale division} = \frac{4 \times {MSD}}{5} = \frac{4 \times 1}{5} = 0.8 \, {mm} \] Now, the reading on the Vernier scale is obtained by adding the main scale reading and the Vernier scale reading:
- The main scale reading is between 20 and 21, so it is 20 mm.
- The Vernier scale reading is 4 times the Vernier scale division, which is \( 4 \times 0.8 = 3.2 \) mm. Thus, the measured value is:
\[ {Measured value} = 20 + 3.2 = 20.8 \, {mm} \]