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State and explain the theorem of perpendicular axis with an example. |
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Answer» Solution :Statement : The moment of inertia about an AXIS perpendicular to TWO other axes acting in the same plane with their point of INTERSECTION being a point on it and the (third) axis passing through the common point, is EQUAL to the sum of moments of inertia about the two axes e.g: `I_z=I_x+I_y` Let M be the mass of the disck of radiusR. M.I. about a point passing through the centre and perpendicular to the plane containing X and Y is `I_z=(MR^2)/(2)` Since X and Y are in the same plane `I_x=I_y` `:." " I_z=I_x+I_y` becomes `I_z=2I_x` HENCE `I_x=(I_z)/(2)=(MR^2)/4` i.e. moment of inertia of a circular disc about the diameter `=(MR^2)/4` 
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