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  • Can someone help me with this, Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

  • Option 1)

    \frac{181}{2} MR^{2}

  • Option 2)

    \frac{19}{2} MR^{2}

  • Option 3)

    \frac{55}{2} MR^{2}

  • Option 4)

    \frac{73}{2} MR^{2}

 

Answers (1)

best_answer

Ip= Io+(7m).(3R)2

   = \left [ \frac{mR^{2}}{2} +6\left [ \frac{mR^{2}}{2}+m.(2R)^{2}\right ]+(7m)(3R)^{2}\right ]

   =\frac{181}{2}mR^{2}

 

Moment of inertia for disc -

I=\frac{1}{2} MR^{2}

 

- wherein

About an axis perpendicular to the plane of disc & passing through its centre .

 

   and

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.

 

 

 


Option 1)

\frac{181}{2} MR^{2}

This is correct

Option 2)

\frac{19}{2} MR^{2}

This is incorrect

Option 3)

\frac{55}{2} MR^{2}

This is incorrect

Option 4)

\frac{73}{2} MR^{2}

This is incorrect

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Plabita

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