Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

Units and Measurements PYQ — JEE Main 2008 · Shift 0 · Q86 with Solution

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Correct answer: D

Two full turns cover $1\,\text{mm}$ on the main scale. So, pitch = distance moved in one full turn:

$\text{Pitch} = \frac{1\,\text{mm}}{2} = 0.5\,\text{mm}$

The circular scale has $50$ divisions.

$\text{Least count} = \frac{\text{Pitch}}{\text{Number of circular divisions}} = \frac{0.5}{50} = 0.01\,\text{mm}$

Main scale reading = $3\,\text{mm}$

Circular scale reading = $35$ divisions

Thus circular contribution is:

$35 \times 0.01 = 0.35\,\text{mm}$

So observed reading is:

$3 + 0.35 = 3.35\,\text{mm}$

Zero error is $-0.03\,\text{mm}$ .

We use:

$\text{True reading} = \text{Observed reading} - \text{Zero error}$

Since zero error is negative,

$\text{True reading} = 3.35 - (-0.03) = 3.38\,\text{mm}$

$\boxed{3.38\,\text{mm}}$

So the correct option is D.