Calculate Centre of Mass
Density = Constant
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Explanation:
Let OX, rod be placed along x - axis
consider a small element AB=x△θ
OA=x & OB=x+dx
mass of element = λ=
L
λ
x
2
∴x= distance of centre of mass from O, the
X=
∫
0
L
dm
∫
0
L
xdm
=
∫
0
L
L
λ0
x
2
dx
∫
0
L
x
L
λ
0
x
2
dx
L
λ0
L
λ0
∫
0
L
x
2
dx
∫
0
L
x
3
dx
=
3
x
3
∣
0
L
4
x
4
∣
0
L
⇒
4
L
4
.
L
3
3
=
4
3L
centre of mass ⇒
4
3L
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