Question
Download Solution PDFAccording to Routh’s law, the moment of inertia for a spherical body about any one axis passing through its center of gravity is given by:
(where A= Area of the plane, M= Mass of the body and S= Sum of the squares of two semi-axis)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Routh's Law
- If a body is symmetrical in shape about all its three axes, then the moment of inertia (I) about any of its three axes which pass through the center of gravity of the body can be written as:
| Moment of Inertia | Shape of Body |
| \(I=\frac{A(or M)x\ S}{5}\) | bodies that are spherical in shape |
| \(I=\frac{A(or M)x\ S}{4}\) | laminas having circular or rectangular shapes |
| \(I=\frac{A(or M)x\ S}{3}\) | for bodies square in shape or rectangular lamina |
where,
A = Area of plane
M= Mass of the body
S = Sum of the squares of two semi-axis
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