Question

(Mechanics) Find the mass center of a wire bent into the form of an isosceles right-angled triangle.

Answer 1

Given :   a wire bent into the form of an isosceles right-angled triangle​

To  Find : mass center of a wire

Solution:

Let say  

Right angle triangle with perpendicular  sides a  

Let say right angle is at origin

( 0 , 0 ) , ( 0 , a) , ( a , 0)  

will be  3 coordinates

Centroid of triangle is mass center

Centroid  =  ( 0 + 0 + a)/3  , ( 0 + a + 0)/3

= ( a/3  , ( a , 3)

But in this case area between triangles sides is empty

Hence mass has not been uniformly distributed over complete triangle

Mass is just on the perimeter of triangle

Sides = a  , a    

& hypotenuse = a√2

Hypotenuse is at 45° with each sides

Hence center of mass will lie at middle of hypotenuse

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