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  • Help me solve this Consider a thin uniform square sheet made of a rigid material. If its side is ‘'a’', mass m and moment of inertia l about one of its diagonals, then :

Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia l about one of its diagonals, then :

  • Option 1)

    I> \frac{ma^{2}}{12}

  • Option 2)

    \frac{ma^{2}}{24}< I< \frac{ma^{2}}{12}

  • Option 3)

    I= \frac{ma^{2}}{12}

  • Option 4)

    I= \frac{ma^{2}}{24}

 

Answers (1)

best_answer

As we learnt in

Moment of inertia for uniform rectangular lamina -

I= \frac{Ml^{2}}{l2}

- wherein

This is about an axis in the plane of the lamina passing through its centre & perpendicular to its breadth.

 

 

For a thin uniform sheet (square)

where I_{1}=I_{2}=I_{3}=\frac{ma^{2}}{12}


Option 1)

I> \frac{ma^{2}}{12}

This is an incorrect option.

Option 2)

\frac{ma^{2}}{24}< I< \frac{ma^{2}}{12}

This is an incorrect option.

Option 3)

I= \frac{ma^{2}}{12}

This is the correct option.

Option 4)

I= \frac{ma^{2}}{24}

This is an incorrect option.

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