Question

Figure 10 - 26shows a uniform metal plate that had been square before 25 %of it was snipped off. Three lettered points are indicated. Rank them according to the rotational inertia of the plate around a perpendicular axis through them, greatest first.

Short answer

The rank of the points having a maximum moment of inertia is$\mathrm{c}>\mathrm{a}>\mathrm{b}$

Step-by-step solution

Step 1: Given data

The figure of 25 % snipped off square-shaped uniform metal plate.

Understanding the concept

We can rank the points according to the moment of inertia using the relation between the moment of inertia and the radius of gyration of the elements.

Formulae are as follows:

$\mathrm{I}={\mathrm{mh}}^2$

Where, h =Radius of gyration, mis mass, I is the moment of inertia.

Determining the rank of the points having a maximum moment of inertia

Here,

$\mathrm{I}={\mathrm{mh}}^2$

So, the final moment of inertia will be maximum for the axis which consists of elements having more h (which are more distant from the axis).

From this, it can be concluded that the moment of inertia about an axis through point c is maximum followed by (a) and then (b).

Rank is,$\mathrm{c}>\mathrm{a}>\mathrm{b}$

Therefore, the points can be ranked according to the moment of inertia about the axis passing through it using its relationship with the radius of gyration.