Question

Consider a mass ' m ' attached to a spring of length ' l ' performing vertical circle.
Find an expression for :

( 1 ) velocity at any point
( 2 ) tension at any point
( 3 ) minimum velocity at the lower - most point for a vertical circle

Answer 1

The tension on the string is equal to the centripetal force on the mass.

Centripetal force on the string :

$centripetal \: force \: = \frac{m {v}^{2} }{r}$

radius is length of the string which is " l ".

Substitute r in the above equation we get,

$centripetal \: force \: = \frac{m {v}^{2} }{l}$

From the above equation we can get the value of velocity at any point,

$value \: of \: velocity \: at \: any \: point = \\ v = \sqrt{ \frac{TL}{m} }$

• At the lowest point the tension is balanced by the weight of the body.

Weight of the body is mass × gravitational pull

• Weight = mg.

Therefore, the tension is " mg "

Substituting the value of F in the above equation we get,

$v \: = \sqrt{ \frac{mgL}{m} }$

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