Ask Question
23 February, 03:52

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?

+3
Answers (1)
  1. 23 February, 06:13
    0
    The moment of inertia of a spherical shell is I = mr²

    If two spheres have the same moment of inertia, then

    I₁ = I₂

    m₁ (r₁) ² = m₂ (r₂) ²

    Solve for the second mass:

    m₂ = m₁ (r₁/r₂) ²

    Given m₁ = 1 kg, r₁ = 2 m, r₂ = 1m,

    m₂ = (1 kg) (2 m / 1 m) ² = 4 kg
Know the Answer?
Not Sure About the Answer?
Get an answer to your 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 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers