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


2 years ago

Susmita
425 Points
							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)/2Use 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/3If it helps please approve.If you find any confusion in following the steps please ask me.thank you.

2 years ago
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### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions