First slide

Moment of intertia

Question

Moment of inertia of a square sheet about one side is I. Then the moment of inertia of the same square sheet about one of its diagonals is

Moderate

A

$\frac{I}{6}$
B

$\frac{I}{3}$
C

$\frac{I}{4}$
D

$\frac{I}{2}$

Solution

(3)
$\begin{array}{l} I t l b e t h e l e n g t h o f e a c h s i d e, T h e n I = \frac{1}{3} m l^{2} \\ ∴ I_{x'} = I_{A B} - m . {(\frac{a}{2})}^{2} \\ = \frac{1}{3} m l^{2} - \frac{1}{4} m a^{2} = \frac{1}{12} m a^{2} \\ B y p e r p e n d i c u l a r a x i s t h e o r e m \\ I_{o} = I_{x i} + I_{y j} = 2 I_{x} \\ A l s o I_{o} = I_{A C} + I_{B O} = 2 I_{A C} \\ ∴ I_{A C} = I_{x} = \frac{1}{12} m x^{2} = \frac{1}{12} \times 3 I = \frac{1}{4} I . \end{array}$

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