Question

66. Like parallel forces act at the vertices A, B and C of a triangle ABC and are proportional to the lengths BC, AC and AB respectively. The centre of the force is at the-


a) centroid b) circum-centre

c) incentre. d) none of these​

Answer 1

Answer:

Like parallel forces act at the vertices A, B and C of a triangle ABC and are proportional to the lengths BC, AC and AB respectively. The centre of the forces is at the

1) Centroid

2) Circum-centre

3) Incentre

4) None of these

Solution: (3) Incentre

Let λa, λb, λc be the forces acting at the points A, B, C respectively.

Let the resultant λ (a + b + c) of these forces acting at a point O inside the triangle ABC. Let AD be perpendicular to BC and OL perpendicular to BC.

The algebraic sum of the moments of the forces about BC = moment of the resultant about BC

λa . AD = λ (a + b + c) . OL

λ (BC . AD) = λ (a + b + c) . OL

2Δ = 2s . OL

OL = Δ / s

OL = r

The centre of the force is at the incentre.

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Answer 2

Answer:

Let λa, λb, λc be the forces acting at the points A, B, C respectively.

Let the resultant λ (a + b + c) of these forces acting at a point O inside the triangle ABC. Let AD be perpendicular to BC and OL perpendicular to BC.

The algebraic sum of the moments of the forces about BC = moment of the resultant about BC

λa . AD = λ (a + b + c) . OL

λ (BC . AD) = λ (a + b + c) . OL

2Δ = 2s . OL

OL = Δ / s

OL = r

The centre of the force is at the in centre.

Explanation:

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