center of mass of a semi circular lamina of radius a whose density varies as square of distance from center is ?
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Answer:
As the wire is uniform, the mass per unit length of the wire is
πR
M
. The mass of the element is, therefore,
dm=(
πR
M
)(Rdθ)=
π
M
dθ
The coordinates of the center of mass are
X=
M
1
∫xdm=
M
1
∫
0
π
(Rcosθ)(
π
M
)dθ=0
Y=
M
1
∫ydm=
M
1
∫
0
π
(Rsinθ)(
π
M
)dθ=
π
2R
Hence, position of center of mass, (0,
π
2R
)
Explanation:
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