A spring balance and an equal-arm beam balance are used to measure an object at a location… — JAMB UTME

A spring balance and an equal-arm beam balance are used to measure an object at a location where the local acceleration due to gravity is $8.0\text{ m s}^{-2}$ . If the spring balance registers a weight of $40\text{ N}$ , what mass will the equal-arm beam balance register at this location?

$5.0\text{ kg}$ Answer
B
$4.0\text{ kg}$
C
$320\text{ kg}$
D
$50\text{ kg}$

Answer

The equal-arm beam balance will register a mass of

5.0\text{ kg}

Weight is given by

W = mg

. Given

W = 40\text{ N}

and

g = 8.0\text{ m s}^{-2}

, the mass of the object is

m = \frac{40}{8.0} = 5.0\text{ kg}

. An equal-arm beam balance balances the unknown mass against standard masses under the exact same local gravitational field, so local gravity cancels out and it accurately measures the object's mass as

5.0\text{ kg}

Step-by-Step Solution

Calculate the true mass of the object from the spring balance reading

m = \frac{W}{g} = \frac{40\text{ N}}{8.0\text{ m s}^{-2}} = 5.0\text{ kg}

Weight is the gravitational force acting on a mass (

W = mg

), so mass equals weight divided by local acceleration due to gravity.

Determine the reading on the equal-arm beam balance

Mass registered =

5.0\text{ kg}

An equal-arm beam balance compares the gravitational force on the unknown mass against standard masses. Because local gravity affects both sides equally, it measures true mass independent of local gravitational acceleration.

Key Concept

Measurement of Mass and Weight

Estimated Time:1m 0s

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