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## A steel ball is whirled on the end of a chain in a horizontal circle of radius R with a constant period T. If the radius of the circle is th

Question

A steel ball is whirled on the end of a chain in a horizontal circle of radius R with a constant period T. If the radius of the circle is then reduced to 0.75R, while the period remains T, what happens to the centripetal acceleration of the ball?

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Physics
1 year
2021-09-04T15:03:40+00:00
2021-09-04T15:03:40+00:00 1 Answers
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## Answers ( )

Answer:The centripetal acceleration will be increased to 1.33 of its initial state.Explanation:## Centripetal acceleration

The

Centripetal accelerationof an object is the acceleration of the object along a circular path moving towards the center of the circular path. The centripetal acceleration is represented in the equation bellow[tex]a_{c} = \frac{V^{2} }{r}[/tex] ……………………………….. 1

where [tex]a_{c}[/tex] is the centripetal acceleration

v is the tangential velocity

and r is the radius.

## How the Change of Radius Affects the Centripetal Acceleration

Reference to equation 1 the centripetal acceleration ( [tex]a_{c}[/tex]) isincrease in the centripetal acceleration. This can be obtained by multiplying the centripetal acceleration by the inverse of 0.75 which is 1.33.

inversely proportional ([tex]y = \frac{k}{x}[/tex])to the radius of the circle or path. this means that when the radiusincreasesthe centripetal accelerationreducesand when the radiusreducesthe centripetal accelerationincreases. The radius was reduced to0.75Rin the question that will amount to1.33[tex]a_{c}[/tex]Therefore, when the radius is reduced by

0.75R, the centripetal acceleration of the steel ball will increase by1.33[tex]a_{c}[/tex].since theperiod is kept constant