Question

A body is moving in a vertical circle of radius R by means of a string. If the ratio of the maximum to the minimum speeds is √3:1, the ratio of the maximum to the minimum tensions in the spring is


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Answer 1

Answer:

good morning friends

Answer 2

Answer:

Let v

1

and v

2

be the velocities at the lowest and the highest points.

∴

v

2

v

1

=

1

3

Conserving energy between the lowest and highest points gives

v

1

2

=v

2

2

+2gh

⇒3v

2

2

=v

2

2

+2gh

⇒v

2

2

=gh

⇒v

1

2

=3gh

h is distance between the lowest and the highest points which is 2r.

h=2r

Tensions at the lowest and highest point

T

1

=

r

mv

1

2

+mg

T

2

=

r

mv

2

2

−mg

⇒

T

2

T

1

=

v

2

2

/r−g

v

1

2

/r+g

⇒

T

2

T

1

=

2gr/r−g

6gr/r+g

⇒

T

2

T

1

=7/1