Question

if the one force is perpendicular to the resultant and the resultant is 1/3rd times than the other force , show that the ratio of the largest force to the smallest force is 3:2root 2?\

Answer 1

Let the forces be F and 3F acting on the particle as shown in the above figure.

F and F are perpendicular.

Let the angle between 3F and horizontal be θ

We have :

3Fsinθ=F

sinθ=1/3

As the resultant force is in vertical direction net horizontal force shoud be zero

3Fcosθ=F

′F = 3F × 2√2/3

F = 2√2F

ratio = 3:2√2

Step-by-step explanation:

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Answer 2

Let the forces be F and 3F acting on the particle as shown in the above figure.

F and F are perpendicular.

Let the angle between 3F and horizontal be θ

We have :

3Fsinθ=F

sinθ=1/3

As the resultant force is in vertical direction net horizontal force shoud be zero

3Fcosθ=F

′F = 3F × 2√2/3

F = 2√2F

ratio = 3:2√2