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The moment of inertia about the axis passing through a point lying on periphery of disc

The moment of inertia about the axis passing through a point lying on periphery of disc Correct Answer <span class="math-tex">\(\frac{3}{2}MR^{2}\)</span>

Correct option:2

Concept:-

Theorems on Moment of Inertia

There are two important theorems on moment of inertia, which enable the moment of inertia of a body to be determined about any general axis.

1. Theorem of Parallel Axes.

2. Theorem of Perpendicular Axes.

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  1. Theorem of Parallel Axes- It is a very useful theorem to relate the moment of inertia of a rigid body (either two or three dimensional) about two parallel axes, in which one passes through the centre of mass.
  • Let us consider two such axes are shown in figure for a body of mass M.

 

  • If the whole mass of a rigid body is kept at same distance x or R from the axis, then moment of inertia is mx2 or mR2, where m is the mass of whole body.

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  • If the whole mass of a rigid body is kept over the axis then, moment of inertia is zero. For example, moment of inertia of a thin rod about an axis passing through the rod is zero.

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Related Questions

According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $$I$$P) is given by (where, A = Area of the section, $$I$$G = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)
According to parallel axis theorem, the moment of inertia of a section about an axis parallel to the axis through center of gravity (i.e. $${I_{\text{P}}}$$) is given by (where, A = Area of the section, $${I_{\text{G}}}$$ = Moment of inertia of the section about an axis passing through its C.G. and h = Distance between C.G. and the parallel axis.)
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