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26 July, 22:17

A solid cylinder with a radius of 4.0 cm has the same mass as a solid sphere of radius R. If the cylinder and sphere have the same moment of inertia about their centers, what is the sphere's radius?

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  1. 27 July, 01:15
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    The radius of the sphere is 4.47 cm

    Explanation:

    Parameter given:

    Radius of cylinder, R = 4.0cm = 0.04m

    The formula for moment of inertia of the cylinder is given as

    I (C) = 1/2 * mr²

    Where I = moment of inertia

    m = mass of cylinder

    r = radius of cylinder

    The moment of inertia of the sphere is given as:

    I (S) = 2/5 * MR²

    Where M = mass of sphere

    R = radius of sphere.

    From the question, I (C) = I (S), hence,

    1/2 * mr² = 2/5 * MR²

    Since m = M

    1/2 * r² = 2/5 * R²

    1/2 * 5/2 * r² = R²

    5/4 r² = R²

    => 5/4 * 0.04² = R²

    => R² = 5/4 * 0.0016 = 0.002

    => R = 0.0447 m = 4.47 cm

    Therefore, radius of the sphere is 4.47 cm
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