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Q.

Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia about an axis perpendicular to its plane and passing through one of its corners

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a

$\frac{2}{3} {ma}^{2}$

b

$\frac{7}{12} {ma}^{2}$

c

$\frac{1}{12} {ma}^{2}$

d

$\frac{5}{6} {ma}^{2}$

answer is D.

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Detailed Solution

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Question Image

$OA = \frac{a}{\sqrt{2}}; I = I_{c} + m {(OA)}^{2}$

$I = \frac{{ma}^{2}}{6} + m {(\frac{a}{\sqrt{2}})}^{2}$

$I = \frac{2}{3} {ma}^{2}$

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Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia about an axis perpendicular to its plane and passing through one of its corners