Question
Download Solution PDFA semicircular lamina has radius R and diameter D. Determine the moment of inertia about the diametrical axis as shown below?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
The moment of inertia of a circular lamina is
\(I = \frac{π }{{64}}{D^4}\) = π(2R)4/64 = πR4/4
The moment of inertia about the diametrical axis semicircular lamina is
= I/2 = (πR4/4)/2 = πR4/8
Additional Information
The formula of the moment of inertia for various other figures is given below.
Moment of inertia of different section:
|
Shape of cross-section |
INA |
Ymax |
Z |
|
Rectangle |
\(I = \frac{{b{d^3}}}{{12}}\) |
\({Y_{max}} = \frac{d}{2}\) |
\(Z = \frac{{b{d^2}}}{6}\) |
|
Circular |
\(I = \frac{π }{{64}}{D^4}\) |
\({Y_{max}} = \frac{d}{2}\) |
\(Z = \frac{π }{{32}}{D^3}\) |
|
Triangular |
\(I = \frac{{B{h^3}}}{{36}}\) |
\({Y_{max}} = \frac{{2h}}{3}\) |
\(Z = \frac{{B{h^2}}}{{24}}\) |
Last updated on May 28, 2025
-> SSC JE notification 2025 for Civil Engineering will be released on June 30.
-> Candidates can fill the SSC JE CE application from June 30 to July 21.
-> The selection process of the candidates for the SSC Junior Engineer post consists of Paper I, Paper II, Document Verification, and Medical Examination.
-> Candidates who will get selected will get a salary range between Rs. 35,400/- to Rs. 1,12,400/-.
-> Candidates must refer to the SSC JE Previous Year Papers and SSC JE Civil Mock Test, SSC JE Electrical Mock Test, and SSC JE Mechanical Mock Test to understand the type of questions coming in the examination.
-> The Staff Selection Commission conducts the SSC JE exam to recruit Junior Engineers in different disciplines under various departments of the Central Government.