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

Option 1)

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

Option 2)

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

Option 3)

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

Option 4)

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

Answers (1)

As we learnt in

Parallel Axis Theorem -

I_{b\: b'}=I_{a\: a'}+mR^{2}

- wherein

b\: b' is axis parallel to a\: a' & a\: a' an axis passing through centre of mass.

 

 

 

i= M\left | \frac{a^{2}+b^{2}}{12} \right |

for square plate it a = b

I=\frac{Ma^{2}}{6}

From Theorem of Parallel axis.

I=I_{0}+mr^{2}=\frac{ma^{2}}{6}+\frac{ma^{2}}{2}

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


Option 1)

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

This is the correct optoin.

Option 2)

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

This is an incorrect option.

Option 3)

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

This is an incorrect option.

Option 4)

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

This is an incorrect option.

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