Ali and hid father sit at the ends of a see-saw, 2 m from the pivot, as shown in figure 5.12. Where should ali's mother sit in order to balance the see-saw?

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closer to the fulcrum

To determine where Ali's mother should sit to balance the see-saw, we need to consider the torques acting on each side of the pivot. Torque is the measure of the force's ability to cause rotational motion.

In this case, the torque on each side of the see-saw is given by the equation:

Torque = Force × Distance

Let's assign variables to the values given in the question. Let the weight (force) of Ali's father be F1 and the weight of Ali be F2. Let's assume that the see-saw is balanced when Ali's mother sits at a distance x from the pivot.

On Ali's side of the see-saw:
Torque1 = F1 × (2 m - x)

On Ali's mother's side:
Torque2 = F2 × x

For the see-saw to be balanced, the torques on both sides of the pivot must be equal:

Torque1 = Torque2

F1 × (2 m - x) = F2 × x

Now we need the ratio of the weights of the father and Ali. Let's assume F1/F2 = k.

This equation then becomes:
k × (2 m - x) = x

Now let's solve for x:

k × 2 m - k × x = x
k × 2 m = (k + 1) × x
x = (k × 2 m) / (k + 1)

So, to balance the see-saw, Ali's mother should sit at a distance of (k × 2 m) / (k + 1) from the pivot.