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Question: Find the MOI of a uniform square plate of mass m and edge a about one of its diagonals. (...

Find the MOI of a uniform square plate of mass m and edge a about one of its diagonals.

(

A

Ma22\frac { \mathrm { Ma } ^ { 2 } } { 2 }

B

Ma23\frac { \mathrm { Ma } ^ { 2 } } { 3 }

C

Ma29\frac { \mathrm { Ma } ^ { 2 } } { 9 }

D

Ma212\frac { \mathrm { Ma } ^ { 2 } } { 12 }

Answer

Ma212\frac { \mathrm { Ma } ^ { 2 } } { 12 }

Explanation

Solution

Iz = Ix + Iy = I1 + I2 = 2Ix = 2I1

or I1 = Ixl = Iz = I1 = Ma212\frac { \mathrm { Ma } ^ { 2 } } { 12 }