A spring balance is calibrated in kilograms at sea level where g = 10.0\text{ m s}^{-2}. A… — JAMB UTME

A spring balance is calibrated in kilograms at sea level where $g = 10.0\text{ m s}^{-2}$ . An object measured with an equal-arm beam balance at sea level is found to have a mass of $36.0\text{ kg}$ . If this object is taken to a high altitude where $g = 9.0\text{ m s}^{-2}$ and suspended from the same spring balance, what reading will the scale of the spring balance display?

$32.4\text{ kg}$ Answer
B
$36.0\text{ kg}$
C
$40.0\text{ kg}$
D
$324.0\text{ kg}$

Answer

The spring balance scale will display a reading of

32.4\text{ kg}

An equal-arm beam balance measures true invariant mass (

36.0\text{ kg}

) by comparing gravitational moments on two arms. A spring balance measures force (weight). At high altitude, the gravitational force acting on the mass is

W = 36.0\text{ kg} \times 9.0\text{ m s}^{-2} = 324\text{ N}

. Because the spring balance scale was calibrated assuming sea-level gravity (

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

), it converts force to indicated mass as

324\text{ N} / 10.0\text{ m s}^{-2} = 32.4\text{ kg}

Step-by-Step Solution

Calculate the true weight of the object at the new altitude

W = m \times g_{\text{altitude}} = 36.0\text{ kg} \times 9.0\text{ m s}^{-2} = 324\text{ N}

Weight is the force of gravity acting on a mass at a specific location.

Determine the indicated mass reading on the calibrated spring balance scale

\text{Reading} = \frac{W}{g_{\text{calibration}}} = \frac{324\text{ N}}{10.0\text{ m s}^{-2}} = 32.4\text{ kg}

The spring balance measures tension force but its scale was calibrated using sea-level gravity (

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

) to indicate mass.

Key Concept

Mass is an intrinsic property measured independently of gravity by a beam balance, whereas weight is a force measured by a spring balance, causing mass-calibrated spring balances to give different readings under varying local gravitational accelerations.

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