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Test Index
JEE Main Physics Class 11 System of Particles and Rotational Motion Part 2 Questions
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© examsnet.com
Question : 64
Total: 100
As shown in fig. when a spherical cavity (centred at
O
) of radius 1 is cut out of a uniform sphere of radius
R
(centred at
C
), the centre of mass of remaining (shaded) part of sphere is at
G
,
i.e on the surface of the cavity.
R
can be determined by the equation:
[8 Jan. 2020 II]
(
R
2
+
R
+
1
)
(
2
−
R
)
=
1
(
R
2
−
R
−
1
)
(
2
−
R
)
=
1
(
R
2
−
R
+
1
)
(
2
−
R
)
=
1
(
R
2
+
R
−
1
)
(
2
−
R
)
=
1
Validate
Solution:
Mass of sphere
=
volume of sphere
x
density of sphere
=
4
3
π
R
3
ρ
Mass of cavity
M
cavity
=
4
3
π
(
1
)
3
ρ
Mass of remaining
M
(Remaining)
=
4
3
π
R
3
ρ
−
4
3
π
(
1
)
3
ρ
Centre of mass of remaining part,
X
COM
=
M
1
r
1
+
M
2
r
2
M
1
+
M
2
⇒
−
(
2
−
R
)
=
[
4
3
π
R
3
ρ
]
0
+
[
4
3
π
(
1
)
3
(
−
ρ
)
]
[
R
−
1
]
4
3
π
R
3
ρ
+
4
3
π
(
1
)
3
(
−
ρ
)
⇒
(
R
−
1
)
(
R
3
−
1
)
=
2
−
R
⇒
(
R
−
1
)
(
R
−
1
)
(
R
2
+
R
+
1
)
=
2
−
R
⇒
(
R
2
+
R
+
1
)
(
2
−
R
)
=
1
© examsnet.com
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