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Question
Physics
Consider a semi-circular disc of mass M and radius R . The moment of inertia of a uniform semi circular disc about an axis passing through its centre of mass and perpendicular to its plane is,
Q. Consider a semi-circular disc of mass
M
and radius
R
. The moment of inertia of a uniform semi circular disc about an axis passing through its centre of mass and perpendicular to its plane is,
98
133
NTA Abhyas
NTA Abhyas 2020
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A
2
M
R
2
+
M
(
3
π
4
R
)
2
B
2
M
R
2
−
M
(
3
π
4
R
)
2
C
2
(
MR
)
2
−
M
(
π
2
R
)
2
D
2
(
MR
)
2
+
M
(
π
2
R
)
2
Solution:
I
0
=
(
2
(
m
R
)
2
)
I
0
=
I
c
m
+
m
d
2
2
m
R
2
=
I
c
m
+
m
(
3
π
4
R
)
2
⇒
I
c
m
=
2
m
R
2
−
m
(
3
π
4
R
)
2
I
c
n
=
[
2
M
R
2
−
M
(
3
π
4
R
)
2
]