what are doing in brainly app all please answer my questions
Answers
Answer:
The correct options are
C The centre of mass of the assembly rotates about the z-axis with an angular speed of
ω
/
5
D The magnitude of angular momentum of the assembly about its centre of mass is
17
m
a
2
ω
/
2
Let the angle of axis with horizontal be
θ
.
c
o
s
θ
=
l
√
l
2
+
a
2
=
√
24
5
(
∵
l
=
√
24
a
)
Distance of centre of mass of the system from O,
l
c
m
=
m
l
+
4
m
(
2
l
)
m
+
4
m
=
9
5
l
Velocity of centre of mass,
V
c
m
=
(
m
×
ω
a
)
+
(
4
m
.
ω
.2
a
)
m
+
4
m
=
9
5
ω
a
Magnitude of angular momentum of centre of mass about point O,
=
(
m
+
4
m
)
V
c
m
l
c
m
=
5
m
×
9
5
ω
a
×
9
5
l
=
81
√
24
5
m
ω
a
2
Hence option B is incorrect.
Now angular momentum
→
L
of entire assembly = Angular momentum of centre of mass system about point O + Angular momentum about the rod connecting two discs
z- component of angular momentum of centre of mass of entire assembly about point O,
→
L
1
=
81
√
24
5
m
ω
a
2
c
o
s
θ
Angular momentum of assembly about the axis passing along rod,
→
L
2
=
[
1
2
m
a
2
+
1
2
(
4
m
)
(
2
a
)
2
]
ω
→
L
2
=
17
2
m
ω
a
2
z-component of
→
L
2
=
17
2
m
ω
a
2
(
−
s
i
n
θ
)
Thus angular momentum of entire assembly about point O,
→
L
=
→
L
1
+
→
L
2
=
81
√
24
5
m
ω
a
2
c
o
s
θ
+
17
2
m
ω
a
2
(
−
s
i
n
θ
)
→
L
=
3803
50
m
ω
a
2
(
∵
c
o
s
θ
=
√
24
5
a
n
d
s
i
n
θ
=
1
5
)
Hence option A is incorrect.
Velocity of point P (center of lower disk)
a
ω
=
l
Ω
Where
Ω
is the angular velocity of centre of mass (C.M) about axis perpendicular to the extension of rod connecting two discs.
Then
Ω
=
a
ω
l
Thus angular velocity of C.M. w.r.t z axis
=
Ω
c
o
s
θ
⇒
ω
C
M
−
z
=
a
ω
l
√
24
5
=
ω
5
Hence option C is correct.
L
D
−
C
M
=
I
1
ω
+
I
2
ω
L
D
−
C
M
=
m
a
2
2
ω
+
4
m
(
2
a
)
2
2
ω
=
17
m
a
2
ω
2
Hence option D is correct.