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Two forces each of magnitude F, acting o a particle yield a resultant force of magnitude F. The angle between the forces is
- a)0o
- b)30o
- c)90o
- d)120o
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two forces each of magnitude F, acting o a particle yield a resultant ...
Using eq. R=√A2+B2+2ABcosθ
where both A and B =F and R=F
By substituting,we get
cosθ=1/2
and
∵ θ=120∘. so, op D.
where both A and B =F and R=F
By substituting,we get
cosθ=1/2
and
∵ θ=120∘. so, op D.
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Two forces each of magnitude F, acting o a particle yield a resultant ...
Given: Two forces each of magnitude F, acting on a particle yield a resultant force of magnitude F.
To find: The angle between the forces.
Solution:
Let's assume the two forces to be F1 and F2, where F1 and F2 are equal in magnitude and act at an angle θ between them.
F1 = F2 = F
The resultant force R can be found using the parallelogram law of forces as shown below:
[Parallelogram law of forces image]
From the figure,
R^2 = F1^2 + F2^2 + 2F1F2cosθ
Since R = F, we can rewrite the above equation as
F^2 = 2F^2 + 2F^2cosθ
On simplifying, we get
cosθ = -1/2
The angle θ can be found using the inverse cosine function as follows:
θ = cos^-1 (-1/2)
Using a calculator, we get θ = 120°
Therefore, the angle between the forces is 120°.
Answer: (d) 120°
To find: The angle between the forces.
Solution:
Let's assume the two forces to be F1 and F2, where F1 and F2 are equal in magnitude and act at an angle θ between them.
F1 = F2 = F
The resultant force R can be found using the parallelogram law of forces as shown below:
[Parallelogram law of forces image]
From the figure,
R^2 = F1^2 + F2^2 + 2F1F2cosθ
Since R = F, we can rewrite the above equation as
F^2 = 2F^2 + 2F^2cosθ
On simplifying, we get
cosθ = -1/2
The angle θ can be found using the inverse cosine function as follows:
θ = cos^-1 (-1/2)
Using a calculator, we get θ = 120°
Therefore, the angle between the forces is 120°.
Answer: (d) 120°
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Two forces each of magnitude F, acting o a particle yield a resultant force of magnitude F. The angle between the forces isa)0ob)30oc)90od)120oCorrect answer is option 'D'. Can you explain this answer?
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