Question

You
mass m and
radius r rolls
maiorig the
following looped
track without
slipping:
What is the
minimum value
of H if the
marble is to
reach the
highest point of
the loop without
leaving the
track?​

Answer 1

Answer:

hey guys

here is your detail answer:-

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

[ R2r 2 ]

I hope it will help you