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A rigid body, whose two of the principal moments of inertia are equal and the third is zero, is called as :

  • A.Asymmetrical top
  • B.Rotor
  • C.Spherical top
  • D.Symmetrical top

Answer: B

Such a body is called a rotor.

When two principal moments are equal and the third is zero (\(I_{A} = 0\), \(I_{B} = I_{C}\)), all the mass lies on one axis, as in a diatomic or linear polyatomic molecule such as HCl or CO\(_{2}\). This is the rigid rotor of rotational spectroscopy, with energy levels \(E_{J} = \frac{\hbar^{2}}{2I}J(J + 1)\).

A symmetric top has two equal moments and a third that is non-zero (\(NH_{3}\)), a spherical top has all three equal (\(CH_{4}\)), and an asymmetric top has all three different (\(H_{2}O\)).

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