Calculate the distance d if the beam is balanced

For a beam to be balanced, the sum of the clockwise moments about the pivot must equal the sum of the anticlockwise moments about the pivot.

• The force on the left side is $9 \text{ N}$ at a distance of $4 \text{ m}$ from the pivot. This creates an anticlockwise moment.
• The force on the right side is $4 \text{ N}$ at an unknown distance $d$ from the pivot. This creates a clockwise moment.

The moment is calculated as Force $\times$ Distance.
For balance:

$$\text{Anticlockwise Moment} = \text{Clockwise Moment}$$ $$F_1 \times d_1 = F_2 \times d_2$$

$$36 \text{ Nm} = 4 \text{ N} \times d$$ $$d = \frac{36 \text{ Nm}}{4 \text{ N}}$$ $$d = 9 \text{ m}$$

The distance $d$ is $\boxed{\text{9 m}}$.