
Applications of Integration 15-51
In the previous case, we assumed the particles to be situated on the x axis. Now assume that the
particles are located at the points in space ( , ), ( , ), , ( , )
n n1 1 2 2
with masses
n1 2
, , , ,
respectively, on the xy plane. Then the moments of masses w.r.t y axis is
M m x
y i i
i
n
=
∑
=1
.
And the moments of masses w.r.t x axis is
M m y
x i i
i
n
=
∑
=1
.
And the coordinates of centre of mass are given as
( , ) , ,x y
M
M
M
M
y
x
=
where
M m
i
i
n
=
∑
=1
is the total mass of the system.
In this section, our main aim is to find the centre of mass of a thin plate with uniform density r.
Let the plate ...