Q.9
Three solid spheres each of mass m and
diameter d are stuck together such that the
lines connecting the centres form an
equilateral triangle of side of length d. The
ratio 1/1A of moment of inertia 10 of the
system about an axis passing the centroid
and about center of any of the spheres IA
and perpendicular to the plane of the
triangle is :
Options
1. 15/13
2. 13/15
3. 13/23
4.23/13
Answers
Answered by
0
Answer:
Refer image.
Moment of inertia (MI) of one sphere about O
I=I
cm
+(OA)
2
×M
I
cm
=
5
2
M(
2
d
)
2
=
10
Md
2
OA=
3
2
(AC×cos30)=
3
2
×d×
2
3
=
3
d
OA=
3
d
I=
10
md
2
+m(
3
d
)
2
=md
2
(
10
1
+
3
1
)
So I
0
=3md
2
(
10
1
+
3
1
)=3md
2
(
30
3+10
)
I
0
=
10
13
md
2
I
A
=
5
2
m(
2
d
)
2
+2[
5
2
m(
2
d
)
2
+md
2
]
=
5
6
m(
2
d
)
2
+2md
2
I
A
=
10
3
md
2
+2md
2
=
10
23
md
2
Ratio
I
A
I
0
=
23/10md
2
13/10md
2
=
23
13
I
A
I
0
=
23
13
Option (B)
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