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JEE Advanced 2020 Full Test 1 Paper 1
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© examsnet.com
Question : 4
Total: 54
A hollow cylinder of radius
4
R
is rotating about fixed horizontal axis passing through point '
O
' with angular velocity
ω
0
. A solid cylinder of radius 'R' is rolling without slipping with respect to inner surface of hollow cylinder. At the given instant, the line OC has angular velocity of
2
ω
0
. Point
A
and
B
are topmost and bottom most point of solid cylinder respectively and
C
is its centre. Then, at the given instant
Angular velocity of solid cylinder about its own axis is
10
ω
0
(
Magnitude of acceleration of point
A
of solid cylinder is
88
ω
0
2
R
(
Magnitude of acceleration of point B of solid cylinder with respect to contact surface of hollow cylinder is
112
ω
0
2
R
(
Radius of curvature of point
A
is
32
R
11
Validate
Solution:
Condition of no. slipping
ω
R
−
6
ω
0
R
=
4
ω
0
R
ω
=
10
ω
0
Acceleration of Point
A
→
a
A
=
→
a
A
,
C
+
→
a
C
↑
12
ω
0
2
R
a
A
=
88
ω
0
2
R
↓
˙
↓
(
10
ω
0
)
2
R
Radius of curvature
ρ
=
v
A
2
a
n
=
(
16
ω
0
R
)
2
88
ω
0
2
R
=
32
R
11
Acceleration of point
B
with respect to surface
(
→
a
B
−
→
a
Sulface
)
→
a
B
=
→
a
B
.
C
+
→
a
C
→
a
S
=
ω
0
2
4
R
=
4
ω
0
2
R
→
a
P
S
=
(
112
−
4
)
ω
0
2
R
=
108
ω
0
2
R
© examsnet.com
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