This question involves the concept of tension, centripetal force, centrifugal force, and weight.
The tension of the stone at the highest point is "0 N".
The centrifugal force always acts away from the circle. The tension always acts toward the support that is the center of the circle in this case. When the stone is at its lowest point, the centrifugal force, and the weight of the stone, both act downward. But the tension is pointing in the upward direction. Hence, the equilibrium equation will be:
[tex]Tension = Weight\ + \ Cenrifugal\ Force\\T = W + F_c\\T = 2\ W\ (given)\\2\ W = W+F_c\\F_c = 2\ W - W\\F_c = W[/tex]
Now, we consider the stone at the top position. Here, the centrifugal force will act in the upward direction (away from the center of the circle), while the weight and tension will be acting in the downward direction. Thus, the equilibrium equation, in this case, will be:
[tex]F_c = W+T\\T=F_c-W\\T = W-W\\[/tex]
T = 0 N
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The attached picture shows the free body diagram of the stone at different locations.
