Home/ Questions/A table tennis ball has a mass of 2.7 g and is 40 mm in diameter.
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lizawr
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Asked: 2022-04-10T08:10:07+00:00 In:

A table tennis ball has a mass of 2.7 g and is 40 mm in diameter.

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A regulation table tennis ball has a mass of 2.7g and is 40mm in diameter. What is its moment of inertia about an axis that passes through its center?

♦ Relevant knowledge
Mass is a measurement unit which describes the amount of matter in an object. It is also the term that defines and measures an object’s inertia, also known as the resistance to change when in motion. In the SI base unit utilized to quantify mass is kilogram (kg) However, the grams (g) can also be employed frequently in the field of science.

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  1. Best Answer

    Concepts and Reason
    This problem can be solved using two concepts: moment of inertia for the hollow sphere, and conversion of units.

    Calculate the mass in kilograms by first dividing the radius of the sphere into its diameter. Substitute the values in the expression for moment of inertia hollow sphere to calculate moment of inertia for the tennis ball around an axis passing through its center.

    Fundamentals

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  2. Concepts and Reason

    This problem can be solved using two concepts: moment of inertia for the hollow sphere, and conversion of units.

    Calculate the mass in kilograms by first dividing the radius of the sphere into its diameter. Substitute the values in the expression for moment of inertia hollow sphere to calculate moment of inertia for the tennis ball around an axis passing through its center.

    Fundamentals

    A sphere’s radius is equal to half its diameter. This is:

    [katex]r = \frac{d}{2}[/katex]

    Here, [katex]r[/katex]

    The moment of inertia for hollow spheres around an axis which passes through its center is

    [katex]I = \frac{2}{3}m{r^2}[/katex]

    Here, [katex]I[/katex]

    These are the relations that covert units use:

    [katex]\begin{array}{c}\\1{\rm{ mm}} = {10^{ – 3}}{\rm{ m}}\\\\1{\rm{ g}} = {10^{ – 3}}{\rm{ kg}}\\\end{array}[/katex]

    The relationship between radius and diameter is.

    [katex]r = \frac{d}{2}[/katex]

    Substitute [katex]40{\rm{ mm}}[/katex]

    [katex]\begin{array}{c}\\r = \frac{{40}}{2}{\rm{ mm}}\\\\ = 20{\rm{ mm}}\\\end{array}[/katex]

    Multiply [katex]\left( {\frac{{{{10}^{ – 3}}{\rm{ m}}}}{{1{\rm{ mm}}}}} \right)[/katex] to convert mm to m

    [katex]\begin{array}{c}\\r = 20{\rm{ mm}}\left( {\frac{{{{10}^{ – 3}}{\rm{ m}}}}{{1{\rm{ mm}}}}} \right)\\\\ = 2.0 \times {10^{ – 2}}{\rm{ m}}\\\end{array}[/katex]

    Convert mass [katex]r[/katex]0

    [katex]r[/katex]1

    The tennis ball’s moment of inertia is described as,

    [katex]I = \frac{2}{3}m{r^2}[/katex]

    Substitute [katex]r[/katex]3

    [katex]r[/katex]4Ans:

    The moment of inertia for the tennis ball around an axis passing through its center is [katex]r[/katex]5

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