Weights of 20N and 80N were suspended from the ends of a 60 cm long rod. At what distance from a lighter

Weights of 20N and 80N were suspended from the ends of a 60 cm long rod. At what distance from a lighter weight should the rod be supported so that it is in a horizontal position.

Let’s translate the values from given to the SI system:
l = 60 cm = 0.6 m.
According to the rule of the lever, the condition for the balance of the lever will be the equality of the moments of forces applied at the ends of the lever:
M1 = M2
The moment of force is equal to the product of the force on the shoulder:
M = F * l
By the equilibrium condition:
F1 * l1 = F2 * l2
F1 / F2 = l2 / l1
Let us express l2 from this expression:
l2 = F1 * l1 / F2
Substituting the numbers, we have:
l2 = (20/80) * l1 = 0.25 * l1.
On the other hand, the length of the rod is:
l = l1 + l2, we substitute l2 into this expression:
l = l1 + 0.25 * l1 = 1.25 * l1
Let us find l1 from this expression:
l1 = l / 1.25 = 0.6 / 1.25 = 0.48 m.
Answer: at a distance of 0.48 m from a lighter weight.