Question:
If the moment of inertia of a disc about an axis tangential and parallel to its surface be $I$, then what will be the moment of inertia about the axis tangential but perpendicular to the surface?
If the moment of inertia of a disc about an axis tangential and parallel to its surface be $I$, then what will be the moment of inertia about the axis tangential but perpendicular to the surface?
Updated On: Jun 20, 2022
- $\frac {6}{5}I$
- $\frac {3}{4}I$
- $\frac {3}{2}I$
- $\frac {5}{4}I$
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The Correct Option is A
Solution and Explanation
MI of disc about tangent in a place
$\hspace5mm = \frac {5}{4}MR^2=I \, MR^2= \frac {4}{5}I$
MI of disc about tangent perpendicular to plane
$\hspace10mm I'= \frac {3}{2}MR^2$
$\hspace10mm I'=\frac {3}{2}\bigg (\frac {4}{5}I\bigg )= \frac {6}{5}I$
$\hspace5mm = \frac {5}{4}MR^2=I \, MR^2= \frac {4}{5}I$
MI of disc about tangent perpendicular to plane
$\hspace10mm I'= \frac {3}{2}MR^2$
$\hspace10mm I'=\frac {3}{2}\bigg (\frac {4}{5}I\bigg )= \frac {6}{5}I$
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