# Question #b15fb

##### 1 Answer

#### Explanation:

Use the fact that the horizontal component of the tension must provide the necessary centripetal force while its vertical component equilibrates with the weight of the ball.

We are not given the radius of the circle. We have to figure that out from the ball's speed and the rope length.

The forces acting on the ball are its weight (

As the ball goes in a horizontal circle, the rope traces a cone with an apex angle

**Vertical Components**: In the vertical direction, weight of the ball equilibrates with the vertical component of the tension.

**Horizontal Components**: The only force on the horizontal direction is the horizontal component of tension and that is the centripetal force making the object move in a circle.

We can write the orbital radius of the ball in terms of the rope length and apex angle as

Comparing (1) and (2),

Let

The solutions to this quadratic equation are -

Since

Now use (1) to solve for