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**Circular momentum - Tension of a string.**

## Homework Statement

A body of mass 1kg is tied to a string and rotates on a horizontal frictionless table. If the length of the string is 40.0 cm and the speed of revolution is 2m/s, find the tension in the string.

**2. The attempt at a solution**

Since the two forces acting on the string is gravity and tension, and the momentum is horizontal, it means that Ty (vertical component of the tension) is equal and opposite to the gravity, and thus, the net force is Tx component (which would thus also be the centripetal force). Hence, we can find the tension of the string by finding the centriputal acceleration, and consequently the magnitude of that force, then use pythagoras theorem to find the tension.

My problem here is that I'm not quite sure about the relation of the length of the string and the radius of the circle around which the mass moves. I tried to hold my hand still whilst drawing a circle with my pencil and noticed that the diameter was very close to the length of the pencil, but I'm not sure if that is enough to assume that the radius must be 20cm. I think that if someone helps me out with this part, I'll most likely be able to solve the question.

EDIT: Another thing which confuses me is that in the book, it says that the magnitude of the tension is 10m. However, As the mass is 1kg, the magnitude of gravity should be 10N, and thus so should the Ty component. That means that the tension has to be at least greater than 10 (as it is the hyoptenuse if we imagine the two components and it as a right-angled triangle).

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