Chapter 8, Problem 86A

To determine

To rank:The objects according to their moment of inertia from least to greatest.

Explanation of Solution

Introduction:

The moment of inertia of an object from the axis of rotation:

  $I=M{r}^2$

Where,

  $r=$ Distance of object from the axis of rotation.

  $M=$ Mass of the object.

According to the formula, the masses that are further away from the axis of rotation has maximum moment of inertia.

Therefore, it can be concluded that greater shaded region would lead to the smaller distance from the axis of rotation and hence, smaller moment of inertia.

The mass of figure E is distributed through all over the radius, therefore the distance of mass E from the axis of rotation would be minimum as compare to the rest of figures. Therefore, it would have minimum moment of inertia.

In figure D, the distance of mass from the axis of rotation would be maximum, therefore it would have greatest moment of inertia.

Therefore, the rank of the moment of inertia from least to greatest:

  $E<B<C<A<D$

Conclusion:

Hence, The rank of the moment of inertia from least to greatest:

  $E<B<C<A<D$