Particle on Elastic String Executing Horizontal

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A particle suspended from an elastic string will extend the string slightly and if the particle is made to move in a horizontal circle, the will be a component of the centripetal force extending the string a little more. To find the extension and the tension in the string, we can resolve vertically and horizontally.

The tension in the string is

Resolving vertically gives (1)

Applying F=ma horizontally gives (2)

(2) divided by (1) gives

Suppose thatandTakethenthenand

(1) givesthen

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