Question

find out the centre of mass of an isosceles triangle of Base length a and altitude b. assume that the mass of the triangle is uniformly distributed over it's area​

Answer 1

To locate the center of mass of the triangle, we take a strip of width dx at a distance x from the vertex of the triangle. Length of this strip can be evaluated by similar triangles as

l = x . (a/b)

Mass of the strip is dm=  

ab

2M

​  

ldx

Distance of center of mass from the vertex of the triangle is

x  

CM

​  

=  

M

1

​  

∫xdm

=∫  

0

b

​  

 

b  

2

 

2x  

2

 

​  

dx

=  

3

2

​  

b

Hence, the center of mass of an isosceles triangle of base length a and altitude b is  

3

2

​  

b