Physics

To find the tension in the string at the top of the vertical circle, we can use the following approach.

 

At the top of the circle, the forces acting on the ball are the gravitational force (weight) and the tension in the string. The centripetal force required to keep the ball moving in a circle is provided by the net force acting towards the center of the circle.

 

The equations involved are:

1. The gravitational force acting on the ball:

where:

 

2. The centripetal force required to keep the ball moving in a circle at speed :

where:

 

Now, calculate the gravitational force:

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