A Vernier caliper with a least count of 0.01\text{ cm} is used to measure the thickness of… — JAMB UTME

A Vernier caliper with a least count of $0.01\text{ cm}$ is used to measure the thickness of a uniform metal plate. When the jaws are closed together without the plate inserted, the zero line of the Vernier scale lies to the right of the main scale zero, with the $3\text{rd}$ Vernier division coinciding with a main scale mark. When clamped around the metal plate, the main scale reading is $1.8\text{ cm}$ and the $4\text{th}$ Vernier division aligns perfectly with a main scale mark. What is the correct thickness of the metal plate?

$1.81\text{ cm}$ Answer
B
$1.84\text{ cm}$
C
$1.87\text{ cm}$
D
$1.77\text{ cm}$

Answer

The correct thickness of the metal plate is

1.81\text{ cm}

When the Vernier zero is positioned to the right of the main scale zero when jaws are closed, it indicates a positive zero error equal to

+ (3 \times 0.01\text{ cm}) = +0.03\text{ cm}

. The observed measurement with the metal plate is

1.8\text{ cm} + (4 \times 0.01\text{ cm}) = 1.84\text{ cm}

. Applying the standard correction formula

\text{Correct Reading} = \text{Observed Reading} - \text{Zero Error}

gives

1.84\text{ cm} - 0.03\text{ cm} = 1.81\text{ cm}

Step-by-Step Solution

Determine the zero error of the Vernier caliper

Zero error

= +3 \times 0.01\text{ cm} = +0.03\text{ cm}

Because the Vernier zero lies to the right of the main scale zero, the instrument has a positive zero error.

Calculate the observed reading

Observed reading

= 1.8\text{ cm} + (4 \times 0.01\text{ cm}) = 1.84\text{ cm}

The total observed value is the sum of the main scale reading and the Vernier scale reading.

Apply the zero error correction to obtain the actual reading

Correct reading

= 1.84\text{ cm} - (+0.03\text{ cm}) = 1.81\text{ cm}

True Reading = Observed Reading - Zero Error (with proper sign).

Key Concept

Vernier Caliper Zero Error Correction

Estimated Time:1m 15s

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