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The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is
- a)120o
- b)60o
- c)90o
- d)150o
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The resultant of two forces, one double the other in magnitude, is per...
Given: Two forces, F and 2F, and the resultant R is perpendicular to F.
To find: The angle between the two forces.
Solution:
Let's assume the angle between F and 2F be θ.
Using the parallelogram law of vectors, we know that the magnitude of the resultant is given by:
R² = F² + (2F)² + 2F.F.cosθ
As R is perpendicular to F, cosθ = 0
Hence, R² = F² + 4F²
R = F√5
Now, let's consider the triangle formed by the two forces, F and 2F, and the resultant R.
Using the Pythagorean theorem, we know that:
R² = F² + (2F)² - 2F.(2F).cosθ
As cosθ = 0, R² = 5F²
Substituting the value of R², we get:
5F² = F² + 4F² - 4F²cosθ
4F²cosθ = 2F²
cosθ = 1/2
θ = 60°
Therefore, the angle between the two forces is 60°.
Answer: (A) 120°
To find: The angle between the two forces.
Solution:
Let's assume the angle between F and 2F be θ.
Using the parallelogram law of vectors, we know that the magnitude of the resultant is given by:
R² = F² + (2F)² + 2F.F.cosθ
As R is perpendicular to F, cosθ = 0
Hence, R² = F² + 4F²
R = F√5
Now, let's consider the triangle formed by the two forces, F and 2F, and the resultant R.
Using the Pythagorean theorem, we know that:
R² = F² + (2F)² - 2F.(2F).cosθ
As cosθ = 0, R² = 5F²
Substituting the value of R², we get:
5F² = F² + 4F² - 4F²cosθ
4F²cosθ = 2F²
cosθ = 1/2
θ = 60°
Therefore, the angle between the two forces is 60°.
Answer: (A) 120°
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Community Answer
The resultant of two forces, one double the other in magnitude, is per...
Equate the component of the force of greater magnitude with smaller force . their anti parallel components will give angle between greater force and resultant .now add this angle with π/2.
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The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces isa)120ob)60oc)90od)150oCorrect answer is option 'A'. Can you explain this answer?
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