**67. A small 0.500-kg object moves on a frictionless horizontal table in a circular path of radius 1.00 m. The angular speed is 6.28 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 105 N, what is the radius of the smallest possible circle on which the object can move?

For an object in orbit,

Now from Sum of forces in radial direction we get

But tangential velocity is

So smallest radius is the greatest tension and it is the “After”

Use the relationship found before

Solve for R_After

Take Cube root

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