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  • I need help with Four identical thin rods each of mass M and length l, form a square frame. Moment of inetia of this frame aboit an axis through the centre of the square and perpendicular to its plane is

Four identical thin rods each of mass M and length l, form a square frame. Moment of inetia of this frame aboit an axis through the centre of the square and perpendicular to its plane is

  • Option 1)

    \frac{2}{3}M1^{2}

  • Option 2)

    \frac{13}{3} M1^{2}

  • Option 3)

    \frac{1}{3}M1^{2}

  • Option 4)

    \frac{4}{3}M1^{2}

 

Answers (1)

best_answer

As learnt in

Paraller 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_{xd}=\frac{M1^{2}}{12}

Thus, moment of Inertia of the frame:

I=\frac{M1^{2}}{12}+\frac{M1^{2}}{4}=\frac{M1^{2}}{3}

Total M.o.I= \frac{4}{3}M1^{2}


Option 1)

\frac{2}{3}M1^{2}

This option is incorrect.

Option 2)

\frac{13}{3} M1^{2}

This option is incorrect.

Option 3)

\frac{1}{3}M1^{2}

This option is incorrect.

Option 4)

\frac{4}{3}M1^{2}

This option is correct.

Posted by

divya.saini

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