Question

prove that minimum velocity required at bottom end of a vertical circular motion is √5gl to complete the round​

Answer 1

Answer:

Lowest Point L (h = 0):

This is the minimum velocity of the body required so that the body looping a loop i.e. to go round the circle once completely. This is the minimum velocity at the lowest point of the vertical circle required for a body looping a loop.

Answer 2

Answer:

Equation of motion:

T−mgcosθ=

R

mV

2

At C, T

C

=0 (minimum case)

⟹

R

mV

c

2

=−mgcos(180

o

)

⟹V

C

2

=Rg

⟹V

C

=

Rg

Using the law of conservation of energy:

E

A

=E

C

2

1

mV

A

2

=

2

1

mV

C

2

+2mgR

⟹

2

V

A

2

=

2

gR

+2gR

⟹V

A

2

=5gR

⟹V

A

=

5gR

Again,

E

A

=E

B

From energy conservation:

2

1

mV

A

2

=

2

1

mV

B

2

+mgR

⟹

2

5

gR=

2

1

V

B

2

+gR

⟹V

B

=

3gR