A marble of mass m and radius r rolls along the following looped track without slipping:>R>What is the minimum value of H if the marble is to reach the highest point of the loop without leaving the track?>0.7 R>2.7R>5.2R>0.2 R
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To just complete the track potential energy at height h
(Point P)=(Kinetic+ potential) energy at H
mgh=2mgR+
2
1
mv
0
2
+
2
1
Iω
0
2
where v
0
is velocity required to complete the loop
R
mv
0
2
=mg⇒v
0
2
=gR
mgh=2mgR+
2
1
mv
0
2
+
2
1
×
5
2
mr
2
×
R
v
0
2
gh=2gR+
2
1
gR+
5
1
R
2
r
2
.gR (ω
0
=
R
v
0
pure rolling)
h=
2
5R
+
5
R
[
R
2
r
2
]
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