A spring balance calibrated in newtons shows an initial pointer reading of +0.4\text{ N} b… — JAMB UTME

A spring balance calibrated in newtons shows an initial pointer reading of $+0.4\text{ N}$ before any load is suspended. When a stone is attached to the balance hook, the pointer indicates $18.4\text{ N}$ . Taking acceleration due to gravity $g = 10\text{ m s}^{-2}$ , what is the actual mass of the stone?

$1.8\text{ kg}$ Answer
B
$1.84\text{ kg}$
C
$1.88\text{ kg}$
D
$18.0\text{ kg}$

Answer

The actual mass of the stone is

1.8\text{ kg}

The spring balance has a systematic positive zero error of

+0.4\text{ N}

. To find the true weight exerted by the stone, this offset must be subtracted from the observed scale reading:

18.4\text{ N} - 0.4\text{ N} = 18.0\text{ N}

. Dividing this true weight by the acceleration due to gravity (

10\text{ m s}^{-2}

) yields the correct mass of

1.8\text{ kg}

Step-by-Step Solution

Determine the true weight by applying zero error correction

W_{\text{true}} = 18.4\text{ N} - 0.4\text{ N} = 18.0\text{ N}

A positive zero error means the scale overstates the load and must be subtracted from the observed reading.

Calculate mass using the relation between weight, mass, and gravitational field strength

m = \frac{W_{\text{true}}}{g} = \frac{18.0\text{ N}}{10\text{ m s}^{-2}} = 1.8\text{ kg}

Weight is equal to mass multiplied by acceleration due to gravity (

W = mg

Key Concept

Measurement of Mass and Weight with Zero Error Correction

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