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State and prove theorem of parallel axis.

Answer» <html><body><p></p>Solution :The moment of <a href="https://interviewquestions.tuteehub.com/tag/inertia-1043176" style="font-weight:bold;" target="_blank" title="Click to know more about INERTIA">INERTIA</a> of a body about any axis is equal to the sum of the moment of inertia of the body about a parallel axis passing through its centre of <a href="https://interviewquestions.tuteehub.com/tag/mass-1088425" style="font-weight:bold;" target="_blank" title="Click to know more about MASS">MASS</a> and the product of its mass and the square of the distance between the two parallel axes. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C07_E01_051_S01.png" width="80%"/> <br/> As shown in figure <a href="https://interviewquestions.tuteehub.com/tag/z-750254" style="font-weight:bold;" target="_blank" title="Click to know more about Z">Z</a> and Z. are two parallel axes separated by a distance a. `therefore OO.=a` <br/> The Z-axis passes through the centre of mass O of the rigid body. <br/> From theorem of parallel axes <br/> `I_(Z)=I_(Z)+Ma^(2)orI_(Z)=I_(C)+M(OO.)^(2)` <br/> where `I_(Z)andI_(Z)` are the moments of inertia of the body about the Z and Z. axes respectively. <br/> M = total mass of the body <br/> a = <a href="https://interviewquestions.tuteehub.com/tag/perpendicular-598789" style="font-weight:bold;" target="_blank" title="Click to know more about PERPENDICULAR">PERPENDICULAR</a> distance between the two parallel axes. <br/> If moment of inertia of object of any <a href="https://interviewquestions.tuteehub.com/tag/shape-1204673" style="font-weight:bold;" target="_blank" title="Click to know more about SHAPE">SHAPE</a> about the axis passing through its centre is given, then moment of inertia about the axis parallel to the axis passing through its centre can be determined.</body></html>


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