Two spherical shells have their mass uniformly distrubuted over the spherical surface. One of the shells has a diameter of 2 meters and a ma

Question

Two spherical shells have their mass uniformly distrubuted over the spherical surface. One of the shells has a diameter of 2 meters and a mass of 1 kilogram. The other shell has a diameter of 1 meter. What must the mass m of the 1-meter shell be for both shells to have the same moment of inertia about their centers of mass? m = nothing kg

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Neala 3 years 2021-08-06T18:05:35+00:00 1 Answers 69 views 0

Answers ( )

  1. thuthao
    0
    2021-08-06T18:06:45+00:00
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    Answer:

    the mass m of the 1-meter shell = 4kg

    Explanation:

    The moment of inertia of a spherical shell is given as;

    I = mr²

    From the question, we want the two sphere’s to have the same moment of inetia: Thus,

    I1 = I2

    Where I1 is the moment of inertia of the first spherical shell while I2 is the moment of Inertia of the second spherical shell.

    Thus;

    m1•r1² = m2•r2²

    Where;

    m1 is mass of the first spherical shell which is 1kg

    r1 is radius of first shell which is = 2/2 = 1

    m2 is mass of the second spherical shell which is unknown.

    r2 is radius of second shell which is = 1/2 = 0.5

    Now,we are are asked to find the mass of the 1m diameter shell and in this case it’s m2.

    Thus, let’s make m2 the subject of the formula;

    m2 = m1 (r1/r2)²

    Plugging in the relevant values ;

    m2 = 1(1/0.5)² = 4kg

    For both to have same moment of inertia, mass of 1m shell must be 4kg

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