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a) The Force F₁ applied at A produces a clockwise moment on the wheel. It can be balanced by applying the force F₂ at B in a direction such that it produces an anticlockwise moment. Therefore the vertical force at B should be applied in the downward direction as shown attached figure. In equilibrium F₁ x OA = F₂ x OO'.
b) Since the perpendicular distance OA of a point of application of force F₁ from O is greater than the perpendicular distance OO' of point of application of the force F₂ from O, so in magnitude, the force F₂ is greater than the force F₁.
c) Moment of force F₁ about O = F₁ * OA (clockwise)
Moment of force F₂ about O = F₂ * OO' (anti clockwise)
When the wheel is in equilibrium position,
Clockwise moment = Anti-clockwise moment
i.e F₁ * OA = F₂ * OO'
∴ F₂ / F₁ = OA / OO' ................(i)
Given,
OA = 2.5 cm and OO' = 2.0 cm
Substituting the values of OA and OO' in eqn. (i) the ratios of force will be:
F₂ / F₁ = 2.5 / 2.0
or, F₂ : F₁ = 5 : 4
Hope It Helps You!
