A chemical balance is used to determine the mass of a metallic sphere, giving a reading of… — JAMB UTME

A chemical balance is used to determine the mass of a metallic sphere, giving a reading of $6.0\text{ kg}$ . The sphere is then suspended from a spring balance at a laboratory where the local acceleration due to gravity is $10\text{ m s}^{-2}$ . If the spring balance reads $-3.0\text{ N}$ before any load is attached, what is the indicated reading on the spring balance when the sphere is suspended?

$57.0\text{ N}$ Answer
B
$63.0\text{ N}$
C
$60.0\text{ N}$
D
$6.0\text{ N}$

Answer

The indicated reading on the spring balance is

57.0\text{ N}

The true weight of the metallic sphere is calculated as

W = mg = 6.0\text{ kg} \times 10\text{ m s}^{-2} = 60.0\text{ N}

. Because the spring balance has an initial zero reading of

-3.0\text{ N}

before any load is attached, the indicated reading when the sphere is hung is

60.0\text{ N} - 3.0\text{ N} = 57.0\text{ N}

Step-by-Step Solution

Calculate the true weight of the metallic sphere

W = mg = 6.0\text{ kg} \times 10\text{ m s}^{-2} = 60.0\text{ N}

Weight is the gravitational force acting on mass.

Set up the zero error relationship for instrument measurement

\text{Actual Weight} = \text{Indicated Reading} - \text{Zero Reading}

The actual physical value equals the observed pointer reading minus the zero reading of the unloaded instrument.

Substitute known values and solve for the indicated reading (

R

)

60.0\text{ N} = R - (-3.0\text{ N}) \implies R = 60.0 - 3.0 = 57.0\text{ N}

Solving the linear relation yields an indicated pointer position of

57.0\text{ N}

Key Concept

Mass versus Weight Measurement and Zero Error Correction

Estimated Time:1m 0s

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