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For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x)=5x2+10x , where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm is
- a)100
- b)105
- c)110
- d)115
Correct answer is option 'C'. Can you explain this answer?
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Understanding the Problem
For a cantilever beam with a given bending moment function M(x) = 5x² + 10x, we need to find the shear force at a specific point (x = 10 mm) along the beam.
Key Concepts
- Bending Moment (M): Represents the internal moment that causes the beam to bend.
- Shear Force (V): Represents the internal force that acts perpendicular to the beam's axis.
Finding Shear Force
To find the shear force (V) at a position x, we can use the relationship between bending moment and shear force:
V(x) = dM/dx
This means we need to differentiate the bending moment function M(x).
Calculate the Derivative
1. Given M(x) = 5x² + 10x
2. Differentiate M with respect to x:
- dM/dx = 10x + 10
Evaluate Shear Force at x = 10 mm
1. Substitute x = 10 mm into the derivative:
- V(10) = 10(10) + 10
- V(10) = 100 + 10
- V(10) = 110 N
Conclusion
Thus, the magnitude of the shear force at x = 10 mm is 110 N, which corresponds to option 'C'. This calculation confirms the internal force acting on the beam at that point, which is crucial for understanding the beam's structural integrity.
For a cantilever beam with a given bending moment function M(x) = 5x² + 10x, we need to find the shear force at a specific point (x = 10 mm) along the beam.
Key Concepts
- Bending Moment (M): Represents the internal moment that causes the beam to bend.
- Shear Force (V): Represents the internal force that acts perpendicular to the beam's axis.
Finding Shear Force
To find the shear force (V) at a position x, we can use the relationship between bending moment and shear force:
V(x) = dM/dx
This means we need to differentiate the bending moment function M(x).
Calculate the Derivative
1. Given M(x) = 5x² + 10x
2. Differentiate M with respect to x:
- dM/dx = 10x + 10
Evaluate Shear Force at x = 10 mm
1. Substitute x = 10 mm into the derivative:
- V(10) = 10(10) + 10
- V(10) = 100 + 10
- V(10) = 110 N
Conclusion
Thus, the magnitude of the shear force at x = 10 mm is 110 N, which corresponds to option 'C'. This calculation confirms the internal force acting on the beam at that point, which is crucial for understanding the beam's structural integrity.
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For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x)=5x2+10x , where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm isa)100b)105c)110d)115Correct answer is option 'C'. 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 For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x)=5x2+10x , where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm isa)100b)105c)110d)115Correct answer is option 'C'. 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 For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x)=5x2+10x , where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm isa)100b)105c)110d)115Correct answer is option 'C'. Can you explain this answer?.
For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x)=5x2+10x , where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm isa)100b)105c)110d)115Correct answer is option 'C'. 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 For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x)=5x2+10x , where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm isa)100b)105c)110d)115Correct answer is option 'C'. 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 For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x)=5x2+10x , where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm isa)100b)105c)110d)115Correct answer is option 'C'. Can you explain this answer?.
Solutions for For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is M(x)=5x2+10x , where x is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at x=10 mm isa)100b)105c)110d)115Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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