Question

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Answer 1

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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!