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Which statement is correct about the vector F in the showing the gravitational nature of the forces?
- a)F= Fcos β + Fcos α + Fcosγ
- b)F= Fsin β + Fcos α + Fcosγ
- c)F= Fcos β + Fsin α + Fcosγ
- d)F= Fcos β + Fcos α + Fsinγ
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which statement is correct about the vector F in the showing the gravi...
As we know the α, β and γ are the angles made by the x, y and z-axis respectively. Thus, is the magnitude of the vector is F, the F= Fcos β + Fcos α + Fcosγ. Which means the force is the resultant of all its axis’ components.
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Which statement is correct about the vector F in the showing the gravi...
Understanding the Gravitational Forces
In the context of gravitational forces, the vector F often represents the resultant force acting on an object due to gravity. The resolution of forces into components is crucial for analyzing the system's behavior.
Components of the Force Vector
The correct expression for the force vector F can be derived from the components of the force acting in different directions. In this case, the angles α, β, and γ represent the angles at which the forces are applied relative to the coordinate axes.
Explanation of Option A
Option A states:
F = Fcos(β) + Fcos(α) + Fcos(γ)
This expression is correct because:
- Cosine Function: The cosine function is used to resolve the force vector into its components along the respective axes (X, Y, Z). The use of cosines indicates that the components are being taken along the horizontal directions.
- Directionality: Each term, Fcos(β), Fcos(α), and Fcos(γ), represents the contribution of the force F in the direction of each angle. This means that the total force F can be calculated by summing these horizontal components.
Why Other Options are Incorrect
- Option B: F = Fsin(β) + Fcos(α) + Fcos(γ) - Incorrect because sine is not used for horizontal components.
- Option C: F = Fcos(β) + Fsin(α) + Fcos(γ) - Incorrect due to the use of sine for the vertical component instead of the horizontal one.
- Option D: F = Fcos(β) + Fcos(α) + Fsin(γ) - Also incorrect for the same reason as above.
In conclusion, the correct representation of the gravitational forces in terms of the vector F is indeed option A, which effectively sums the horizontal components of the gravitational force.
In the context of gravitational forces, the vector F often represents the resultant force acting on an object due to gravity. The resolution of forces into components is crucial for analyzing the system's behavior.
Components of the Force Vector
The correct expression for the force vector F can be derived from the components of the force acting in different directions. In this case, the angles α, β, and γ represent the angles at which the forces are applied relative to the coordinate axes.
Explanation of Option A
Option A states:
F = Fcos(β) + Fcos(α) + Fcos(γ)
This expression is correct because:
- Cosine Function: The cosine function is used to resolve the force vector into its components along the respective axes (X, Y, Z). The use of cosines indicates that the components are being taken along the horizontal directions.
- Directionality: Each term, Fcos(β), Fcos(α), and Fcos(γ), represents the contribution of the force F in the direction of each angle. This means that the total force F can be calculated by summing these horizontal components.
Why Other Options are Incorrect
- Option B: F = Fsin(β) + Fcos(α) + Fcos(γ) - Incorrect because sine is not used for horizontal components.
- Option C: F = Fcos(β) + Fsin(α) + Fcos(γ) - Incorrect due to the use of sine for the vertical component instead of the horizontal one.
- Option D: F = Fcos(β) + Fcos(α) + Fsin(γ) - Also incorrect for the same reason as above.
In conclusion, the correct representation of the gravitational forces in terms of the vector F is indeed option A, which effectively sums the horizontal components of the gravitational force.
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Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer?.
Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer?.
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Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Which statement is correct about the vector F in the showing the gravitational nature of the forces?a)F= Fcos β + Fcos α + Fcosγb)F= Fsin β + Fcos α + Fcosγc)F= Fcos β + Fsin α + Fcosγd)F= Fcos β + Fcos α + FsinγCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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