prove that minimum velocity required at bottom end of a vertical circular motion is √5gl to complete the round
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Answered by
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.
Answered by
0
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
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