A uniform solid sphere has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere’s moment of inertia about a

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A uniform solid sphere has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere’s moment of inertia about a central axis?

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Thiên Hương 4 years 2021-09-05T02:59:57+00:00 1 Answers 40 views 0

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  1. ngochoa
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    2021-09-05T03:01:36+00:00
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    Answer:

    The moment of inertia about central axis becomes 18 times to its original moment of inertia when its mass doubled and radius tripled, I₁ = 18I.

    Explanation:

    Moment of inertia of a uniform solid sphere about its central axis is given by the relation :

    I=\frac{2}{5}MR^{2}    ….(1)

    Here I is moment of inertia, M is mass of the solid sphere and R is the radius of the solid sphere.

    Now, the mass of the sphere becomes twice and radius becomes thrice i.e.

    New mass of sphere = 2M

    New radius of new sphere = 3R

    The new moment of inertia is:

    I_{1} =\frac{2}{5}(2M)(3R)^{2}

    I_{1} =\frac{2}{5}\times18MR^{2}

    Substitute equation (1) in the above equation.

    I_{1} =18I

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