Class 12 Exam > Class 12 Questions > Forces of magnitudes 3,P,5,10 and Q are respe...
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Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.?
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Forces of magnitudes 3,P,5,10 and Q are respectively acting along the ...
Given information:
- Magnitudes of forces: 3, P, 5, 10, and Q
- Forces act along the sides AB, BC, CD, AD, and the diagonal CA of a rectangle ABCD
- Length of AB = 4 m
- Length of BC = 3 m
To find:
- Magnitudes of forces P, Q, and the resultant force along diagonal BD
Solution:
Step 1: Analysis of forces
To find the resultant force, we need to analyze the forces acting along the sides and diagonal of the rectangle. Let's analyze each force individually.
Force of magnitude 3 along AB:
- This force acts along the side AB of the rectangle ABCD.
- Since AB is parallel to BD, this force does not contribute to the vertical component of the resultant force along BD.
- Therefore, we only need to consider the horizontal component of this force.
Force of magnitude P along BC:
- This force acts along the side BC of the rectangle ABCD.
- Since BC is perpendicular to BD, this force only contributes to the vertical component of the resultant force along BD.
- Therefore, we only need to consider the vertical component of this force.
Force of magnitude 5 along CD:
- This force acts along the side CD of the rectangle ABCD.
- Since CD is parallel to BD, this force does not contribute to the vertical component of the resultant force along BD.
- Therefore, we only need to consider the horizontal component of this force.
Force of magnitude 10 along AD:
- This force acts along the side AD of the rectangle ABCD.
- Since AD is perpendicular to BD, this force only contributes to the vertical component of the resultant force along BD.
- Therefore, we only need to consider the vertical component of this force.
Force of magnitude Q along the diagonal CA:
- This force acts along the diagonal CA of the rectangle ABCD.
- Since CA is neither parallel nor perpendicular to BD, this force contributes to both the horizontal and vertical components of the resultant force along BD.
- Therefore, we need to consider both the horizontal and vertical components of this force.
Step 2: Calculation of horizontal and vertical components
Let's calculate the horizontal and vertical components of the forces along BC, AD, and CA.
Force P along BC:
- Since BC is perpendicular to BD, the vertical component of force P is equal to its magnitude.
- Therefore, the vertical component of force P is P.
Force 10 along AD:
- Since AD is perpendicular to BD, the vertical component of force 10 is equal to its magnitude.
- Therefore, the vertical component of force 10 is 10.
Force Q along the diagonal CA:
- To calculate the horizontal component of force Q, we need to find the cosine of the angle between CA and BD.
- Let's consider angle θ between CA and BD. Since ABCD is a rectangle, θ = 90 degrees.
- Therefore, the horizontal component of force Q is Q * cos(θ) = Q * cos(90 degrees) = 0.
- To calculate the vertical component of force Q, we need to find the sine of the angle between CA and BD
- Magnitudes of forces: 3, P, 5, 10, and Q
- Forces act along the sides AB, BC, CD, AD, and the diagonal CA of a rectangle ABCD
- Length of AB = 4 m
- Length of BC = 3 m
To find:
- Magnitudes of forces P, Q, and the resultant force along diagonal BD
Solution:
Step 1: Analysis of forces
To find the resultant force, we need to analyze the forces acting along the sides and diagonal of the rectangle. Let's analyze each force individually.
Force of magnitude 3 along AB:
- This force acts along the side AB of the rectangle ABCD.
- Since AB is parallel to BD, this force does not contribute to the vertical component of the resultant force along BD.
- Therefore, we only need to consider the horizontal component of this force.
Force of magnitude P along BC:
- This force acts along the side BC of the rectangle ABCD.
- Since BC is perpendicular to BD, this force only contributes to the vertical component of the resultant force along BD.
- Therefore, we only need to consider the vertical component of this force.
Force of magnitude 5 along CD:
- This force acts along the side CD of the rectangle ABCD.
- Since CD is parallel to BD, this force does not contribute to the vertical component of the resultant force along BD.
- Therefore, we only need to consider the horizontal component of this force.
Force of magnitude 10 along AD:
- This force acts along the side AD of the rectangle ABCD.
- Since AD is perpendicular to BD, this force only contributes to the vertical component of the resultant force along BD.
- Therefore, we only need to consider the vertical component of this force.
Force of magnitude Q along the diagonal CA:
- This force acts along the diagonal CA of the rectangle ABCD.
- Since CA is neither parallel nor perpendicular to BD, this force contributes to both the horizontal and vertical components of the resultant force along BD.
- Therefore, we need to consider both the horizontal and vertical components of this force.
Step 2: Calculation of horizontal and vertical components
Let's calculate the horizontal and vertical components of the forces along BC, AD, and CA.
Force P along BC:
- Since BC is perpendicular to BD, the vertical component of force P is equal to its magnitude.
- Therefore, the vertical component of force P is P.
Force 10 along AD:
- Since AD is perpendicular to BD, the vertical component of force 10 is equal to its magnitude.
- Therefore, the vertical component of force 10 is 10.
Force Q along the diagonal CA:
- To calculate the horizontal component of force Q, we need to find the cosine of the angle between CA and BD.
- Let's consider angle θ between CA and BD. Since ABCD is a rectangle, θ = 90 degrees.
- Therefore, the horizontal component of force Q is Q * cos(θ) = Q * cos(90 degrees) = 0.
- To calculate the vertical component of force Q, we need to find the sine of the angle between CA and BD
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Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.?
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Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.?.
Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.?.
Solutions for Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.? in English & in Hindi are available as part of our courses for Class 12.
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Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.?, a detailed solution for Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.? has been provided alongside types of Forces of magnitudes 3,P,5,10 and Q are respectively acting along the sides AB,BC,CD,AD and the diagonal CA of a rectangle ABCD, where AB=4 m and BC =3 m. if the resultant is a single force along the other diagonal BD , then P,Q and the resultant are.? theory, EduRev gives you an
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