Two forces of 10 N and 40 N act vertically downward at endpoints of a horizontal rod of 120 mm length. The location of the resultant force on the rod is

Concept:

Let the length of the rod be 'L' and 'x' be the distance between the resultant force and smaller force, therefore the distance between the larger force and resultant will be (L - x)

According to the principle of moments:

"The algebraic sum of the moments of all the forces about any point is equal to the moment of their resultant force about the same point.”

Calculation:

Given:

F₁ = 10 N, F₂ = 40 N, L = 120 mm.

When we calculate the moment about the point of the resultant force, then the moment produced by two forces will be equal and opposite.

F1 × x = F2 × (L - x)

10 × x = 40 × (120 - x)

10x = 4800 - 40x

50x = 4800

x = 96 mm.

∴ the distance between the smaller force and the resultant is 96 mm.