Match each length measurement instrument setup on the left with its corresponding true (co… — JAMB UTME

Match each length measurement instrument setup on the left with its corresponding true (corrected) measurement value on the right.

A micrometer screw gauge (pitch $0.5\text{ mm}$ , 50 thimble divisions) with a positive zero error of $+0.04\text{ mm}$ , showing a main scale reading of $2.5\text{ mm}$ and the 28th thimble division aligning. $2.74\text{ mm}$
A Vernier caliper (least count $0.01\text{ cm}$ ) with a negative zero error of $-0.02\text{ cm}$ , showing a main scale reading of $3.4\text{ cm}$ and the 6th Vernier division aligning. $3.48\text{ cm}$
A metre rule (least count $0.1\text{ cm}$ ) used to measure the length of a wooden rod whose ends align with the $2.3\text{ cm}$ mark and the $14.8\text{ cm}$ mark. $12.5\text{ cm}$
A micrometer screw gauge (least count $0.01\text{ mm}$ ) with a negative zero error of $-0.03\text{ mm}$ , showing a main scale reading of $1.5\text{ mm}$ and the 45th thimble division aligning. $1.98\text{ mm}$

The correct pairings match each instrument's corrected reading: micrometer with positive zero error to

2.74\text{ mm}

, Vernier caliper with negative zero error to

3.48\text{ cm}

, metre rule measurement to

12.5\text{ cm}

, and micrometer with negative zero error to

1.98\text{ mm}

Each instrument pairing correctly applies the instrument's least count formula and the standard zero error relationship:

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

Calculate the corrected reading for the first micrometer screw gauge.

Least count =

0.01\text{ mm}

. Observed =

2.5\text{ mm} + 0.28\text{ mm} = 2.78\text{ mm}

. Corrected reading =

2.78\text{ mm} - 0.04\text{ mm} = 2.74\text{ mm}

True Reading = Observed Reading - (Zero Error).

Calculate the corrected reading for the Vernier caliper.

Observed =

3.4\text{ cm} + 0.06\text{ cm} = 3.46\text{ cm}

. Corrected reading =

3.46\text{ cm} - (-0.02\text{ cm}) = 3.48\text{ cm}

Subtracting a negative zero error is equivalent to adding the absolute error magnitude.

Calculate the length of the wooden rod measured with the metre rule.

Length =

14.8\text{ cm} - 2.3\text{ cm} = 12.5\text{ cm}

Subtracting the initial scale alignment point from the final scale alignment point eliminates end-wear errors.

Calculate the corrected reading for the second micrometer screw gauge.

Observed =

1.5\text{ mm} + 0.45\text{ mm} = 1.95\text{ mm}

. Corrected reading =

1.95\text{ mm} - (-0.03\text{ mm}) = 1.98\text{ mm}

Subtracting the negative zero error compensates for the instrument reading below zero prior to measurement.

Instrument Least Count and Zero Error Corrections

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