Question

2) If a person with point mass is tied to a string and a revolved in a vertical circular motion, at what position

the person will have maximum velocity?​

Answer 1

Explanation:

Let velocity at A=v

A

and velocity at B=v

B

Applying conservation of energy at A and B

2

1

mv

2

+2gmr=

2

1

mv

B

2

[∵(P.E.)=mg(2r)]

v

B

2

=v

A

2

+4gr......(i)

Now as it is moving in circular path it has centripetal force.

At point A⇒T+mg=

r

mv

A

2

for minimum velocity T≥0

Or

r

mv

A

2

≥mg⇒v

A

2

≥gr⇒v

a

≥

gr

I hope it helps you ☺️

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Answer 2

If a person with point mass is tied to a string and revolved in a vertical circular motion, at the top of the circle the person will have maximum velocity.

• When the object is at the top of the circle. the tension in the string is given as,

        $T_{1} = \frac{mv^{2} }{R} - mg$

• At that position of motion, the tension in the string is the lowest and hence, the velocity of the person with point mass is maximum.
• This is because a part of the required centripetal force is provided by the weight of the person and the rest by the tension in the string.