- #1

Benjamin_harsh

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- Homework Statement
- Ratio of moment of inertia of a circle and that of a square having same area about their centroidal axis is:

- Relevant Equations
- Why they calculated ##\large\frac{d}{a}## in first step?

Ratio of moment of inertia of a circle and that of a square having same area about their centroidal axis is:

Sol: both area and square have same area:

##a^2 = \large\frac{π}{4}\normalsize d^{2}; \large\frac{d}{a} =\large \sqrt\frac{4}{p}##

Ratio of moment of inertia of a circle and that of a square about their centroidal axis is:

##\large\frac{I_{c}}{I_{s}} = \large\frac{\frac{π}{64}d^4}{\frac{a^{4}}{12}} = \large\frac{12π}{64}\frac{d}{a}^{4}##

##\large\frac{3π}{16}(\sqrt\frac{4}{p})^{4} = \frac{3}{π}##

Sol: both area and square have same area:

##a^2 = \large\frac{π}{4}\normalsize d^{2}; \large\frac{d}{a} =\large \sqrt\frac{4}{p}##

Ratio of moment of inertia of a circle and that of a square about their centroidal axis is:

##\large\frac{I_{c}}{I_{s}} = \large\frac{\frac{π}{64}d^4}{\frac{a^{4}}{12}} = \large\frac{12π}{64}\frac{d}{a}^{4}##

##\large\frac{3π}{16}(\sqrt\frac{4}{p})^{4} = \frac{3}{π}##