In step 1, how did u know that r=......

Imagine the suspension point at the top, and the two threads hanging down, each attached to a ball. The angle between the two threads is given as $60^\circ$.

If you draw a vertical line straight down from the suspension point, it will bisect the angle between the threads and also bisect the distance between the two balls.
This creates two identical right-angled triangles.

• The hypotenuse of each right-angled triangle is the length of the thread, $L$.
• The angle between the thread and the vertical line is $\theta$. Since the total angle between the threads is $60^\circ$, then $\theta = \frac{60^\circ}{2} = 30^\circ$.
• The side opposite to this angle $\theta$ is half the distance between the balls. Let's call this half-distance $x$.

In a right-angled triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse:

Solving for $x$:

The total distance $r$ between the two balls is twice this half-distance $x$:

Substituting the expression for $x$:

In the problem, $L = 0.100 \text{ m}$ and $\theta = 30^\circ$.