Question
Download Solution PDFThe moment of inertia of a circular area about its diameter is Ixx. The moment of inertia of the same circular area about an axis perpendicular to the plane of the area is Izz. Which of the following statements is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Moment of inertia of different section:
|
S.No. |
Shape of cross-section |
INA |
Ymax |
Z |
|
1 |
Rectangle |
\(I = \frac{{b{d^3}}}{{12}}\) |
\({Y_{max}} = \frac{d}{2}\) |
\(Z = \frac{{b{d^2}}}{6}\) |
|
2 |
Circular |
\(I = \frac{\pi }{{64}}{D^4}\) |
\({Y_{max}} = \frac{d}{2}\) |
\(Z = \frac{\pi }{{32}}{D^3}\) |
|
3 |
Triangular |
\(I = \frac{{B{h^3}}}{{36}}\) |
\({Y_{max}} = \frac{{2h}}{3}\) |
\(Z = \frac{{B{h^2}}}{{24}}\) |
For circular cross-section,
\({{I}_{xx}}={{I}_{yy}}=\frac{\pi {{D}^{4}}}{64}\)
According to perpendicular axis theorem,
Izz = Ixx + Iyy
∴ Izz = 2 × Ixx
∴ Ixx is always less than Izz
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