A spring balance suspended inside an elevator reads 48\text{ N} when supporting an object … — JAMB UTME

A spring balance suspended inside an elevator reads $48\text{ N}$ when supporting an object while the elevator accelerates downwards at $2\text{ m s}^{-2}$ . Taking acceleration due to gravity $g = 10\text{ m s}^{-2}$ , what is the mass of the object as measured by an equal-arm beam balance?

$6.0\text{ kg}$ Answer
B
$4.0\text{ kg}$
C
$4.8\text{ kg}$
D
$60.0\text{ kg}$

Answer

The mass of the object measured by an equal-arm beam balance is

6.0\text{ kg}

In a downward accelerating elevator, the apparent weight indicated by a spring balance is

W_{app} = m(g - a)

. Substituting

48\text{ N} = m(10\text{ m s}^{-2} - 2\text{ m s}^{-2}) = 8m

gives a mass of

6.0\text{ kg}

. Because a beam balance compares masses directly and both sides experience the exact same effective acceleration, it measures true mass regardless of the frame's acceleration.

Step-by-Step Solution

Formulate the equation for apparent weight in a downward accelerating reference frame.

W_{app} = m(g - a)

When an elevator accelerates downward, the effective acceleration experienced by an object inside is

(g - a)

Substitute the given values (

W_{app} = 48\text{ N}

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

a = 2\text{ m s}^{-2}

) into the formula to find mass

m

48 = m(10 - 2) \implies 48 = 8m \implies m = 6.0\text{ kg}

This yields the true scalar mass of the object.

Determine the reading on an equal-arm beam balance.

The beam balance reads

6.0\text{ kg}

A beam balance compares unknown mass against standard counter-weights; both experience identical effective acceleration, making its measurement independent of motion or local gravity.

Key Concept

Apparent weight in an accelerating frame vs invariant mass measurement using a beam balance

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