Question

The figure shows a wheel of radius 5 cm that can rotate freely about the point O. It is in equilibrium due to the forces F₁ and F₂ acting on it. Which one of the forces F₁ and F₂ is the greater force? What is the ratio of the two forces? Given OO' = 3 cm.

Answer 1

Given Data:

Perpendicular distance for force F₁ (Radius of the wheel, d₁) = 5 cm

Perpendicular distance for force F₂ (d₂ = OO') = 3 cm

1. According to the condition of equilibrium, the magnitudes of moments of both forces about pivot O must be equal:

Magnitude of moment due to F1 = Magnitude of moment due to F₂

F₁ × d₁ = F₂ × d₂

Since the force applied is inversely proportional to its perpendicular distance from the pivot point:

F₁ acts at a larger distance (5 cm).

F₂ acts at a smaller distance (3 cm).

Therefore, F₂ is the greater force.

2. Using the equilibrium equation:

F₁ × 5 = F₂ × 3

Rearranging the terms to find the ratio:

`F_1/F_2 = 3/5`