Question

1. Locate the centroid of a T-section 10 cm x 10 cm x 2 cm.​

Answer 1

Concept:

The centroid is the centre of mass of a geometric body having uniform density. A body's centroid is the location where all of its sides have the same volume. The centre of mass in a solid body consisting of a single material is known as the centroid. The centroid and centre of mass are identical if the mass of a body is dispersed uniformly.

The T-section consists of two rectangles and it is symmetrical about the y-axis.

Given:  

In the figure attached for the T-section, the sides of the larger rectangle is: 10 and 2 cm.

The sides of the smaller rectangle is: 8 and 2 cm.

To find:

The centroid of the T-section

Solution:

Two rectangles make up a T-section.

Large Rectangle's area= 10×2 = 20 $cm^{2}$.

Smaller Rectangle's area=8×2=16 $cm^{2}$.

Summation of the area will be: 20+16=36 $cm^{2}$

Regarding the reference x-axis, the centroid of the large rectangle is equal to Y= $\frac{16}{2} =8 cm$

Regarding the reference x-axis, the centroid of the smaller rectangle is:

Y=$\frac{2}{2} +16=17 cm$

Moment of area of the larger rectangle, $M_{1}$=20×8=160 cubic cm

Moment of the area of the smaller rectangle, $M_{2}$=16×17=272 cubic cm

Sum of the moments= 160+272= 432 cubic cm.

Now, the centroid of the system $Y'$= $\frac{Sum of moments}{ sum of area}$

Implies that,

$Y'=\frac{432}{36} =12 cm$

Hence, the centroid of the T-section is located at 12 cm.

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