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BITSAT 2022 Paper
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Section:
Physics
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© examsnet.com
Question : 11
Total: 130
Four holes of radius
5
c
m
are cut from a thin square plate of
20
c
m
and mass
1
k
g
. The moment of inertia of the remaining portion about
Z
-axis is
15
‌
kg
−
m
2
0.37
‌
kg
−
m
2
0.0017
‌
kg
−
m
2
0.08
‌
kg
−
m
2
Validate
Solution:
👈: Video Solution
Area mass density,
σ
=
M
16
R
2
(
∵
Area
=
4
R
×
4
R
=
16
R
2
)
Mass of each hole
m
1
=
σ
Ï€
R
2
=
M
16
R
2
Ï€
R
2
=
Ï€
M
16
Distance between centre of plate and centre of hole
x
=
√
(
2
R
)
2
+
(
2
R
)
2
2
=
2
√
2
R
2
Moment of inertia of one hole at about Z-axis
I
1
=
1
2
m
1
R
2
+
m
1
x
2
=
5
Ï€
32
M
R
2
Moment of inertia of whole plate about Z-axis,
I
=
M
(
4
R
)
2
6
=
8
3
M
R
2
Required moment of Inertia
I
0
=
I
−
4
I
1
,
=
[
8
3
−
4
(
5
Ï€
32
)
]
M
R
2
=
[
8
3
−
5
Ï€
8
]
M
R
2
Given, R=5cm and M=1kg
So,
I
0
[
8
3
−
5
Ï€
8
]
1
×
25
×
10
−
4
=
0.0017
k
g
−
m
2
© examsnet.com
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