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Pls let me know the proof how the centre of mass of triangular laminar is h/3.

Pls let me know the proof how the centre of mass of triangular laminar is h/3. 

Grade:11

1 Answers

Susmita
425 Points
5 years ago
Depends on what kind of lamina you are considering.If all 3 sides equal,then follow the steps.
Draw x,y axis.Draw the triangle with vertex at (0,h),(-h/2,0),(h/2,0).
Now draw a strip inside the triangle made of two straight lines parallel to x axis at a height (0,y) and (0,y+dy).
Area of this strip is 2xydy.
Let d is surface density of mass of triangle.
Then the formula of com 
Y=\frac{\int d.y.dS}{\int d.dS}
dS is the area.
Y=\frac{\int_{0}^{h} y.2xydy}{\int_{0}^{h} 2xydy}
Now the side on the right side of y axis passes through (0,h) and (h/2,0).Equation of it is
\frac{x-h/2}{0-h/2}=\frac{y-0}{h-0}
Or,x=(h-y)/2
Use this value of x is the integration.carry it out.
The numeration will give h3/6 and the denominator will give h2/2.
So the result will be Y=h/3
If it helps please approve.If you find any confusion in following the steps please ask me.thank you.
 

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