In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with reference line. Calculate the true reading.

Units and Measurements PYQ — JEE Main 2021 · 26 Aug · Shift 1 · Q57 with Solution

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Correct answer: C

Find the least count of the screw gauge

Given:

Circular scale divisions $= 50$
Pitch (main scale movement in one complete rotation) $= 0.5\,\text{mm}$

So, least count is

\text{L.C.} = \frac{\text{Pitch}}{\text{No. of circular scale divisions}} = \frac{0.5}{50} = 0.01\,\text{mm}

Determine the zero error

When the ratchet is fully closed, the 5th division of the circular scale coincides with the reference line.

That means the screw gauge does not read zero when closed. Since the coinciding division is 5, the zero reading is

5 \times 0.01 = 0.05\,\text{mm}

This is a positive zero error (instrument shows a positive reading when it should read zero).

Hence, zero correction is

-0.05\,\text{mm}

Calculate the observed reading

Given observation:

Main scale reading $= 5\,\text{mm}$
Circular scale reading $= 20$

Circular scale contribution:

20 \times 0.01 = 0.20\,\text{mm}

Observed reading:

5.00 + 0.20 = 5.20\,\text{mm}

Apply zero correction

True reading is

\text{True reading} = \text{Observed reading} + \text{Zero correction}

= 5.20 + (-0.05)

= 5.15\,\text{mm}

Match with the options

$5.15\,\text{mm}$ corresponds to:

Option C

Final Answer: $\boxed{5.15\,\text{mm}}$

More from Units and Measurements

View written solutionFree

Correct answer: C

Find the least count of the screw gauge

Given:

Circular scale divisions $= 50$
Pitch (main scale movement in one complete rotation) $= 0.5\,\text{mm}$

So, least count is

\text{L.C.} = \frac{\text{Pitch}}{\text{No. of circular scale divisions}} = \frac{0.5}{50} = 0.01\,\text{mm}

Determine the zero error

When the ratchet is fully closed, the 5th division of the circular scale coincides with the reference line.

That means the screw gauge does not read zero when closed. Since the coinciding division is 5, the zero reading is

5 \times 0.01 = 0.05\,\text{mm}

This is a positive zero error (instrument shows a positive reading when it should read zero).

Hence, zero correction is

-0.05\,\text{mm}

Calculate the observed reading

Given observation:

Main scale reading $= 5\,\text{mm}$
Circular scale reading $= 20$

Circular scale contribution:

20 \times 0.01 = 0.20\,\text{mm}

Observed reading:

5.00 + 0.20 = 5.20\,\text{mm}

Apply zero correction

True reading is

\text{True reading} = \text{Observed reading} + \text{Zero correction}

= 5.20 + (-0.05)

= 5.15\,\text{mm}

Match with the options

$5.15\,\text{mm}$ corresponds to:

Option C

Final Answer: $\boxed{5.15\,\text{mm}}$

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