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A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is
- a)1/μ
- b)1/μ+1
- c)μl/μ+1
- d)μl/μ-1
Correct answer is option 'C'. Can you explain this answer?
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A uniform rope of length l lies on a table. If the coefficient of fric...
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A uniform rope of length l lies on a table. If the coefficient of fric...
Finding the maximum length of rope overhanging from a table
Given:
- Length of rope = l
- Coefficient of friction =
To find:
- Maximum length of rope that can overhang from the table without sliding down.
Solution:
Let l1 be the maximum length of the rope that can overhang from the table without sliding down. We need to find the value of l1.
Consider the free body diagram of the rope as shown below:
The weight of the rope acts downward and can be resolved into two components:
- F1 = mgcosθ acts perpendicular to the table surface
- F2 = mgsinθ acts parallel to the table surface
The maximum value of friction force that can act on the rope is given by:
f = μN
where, μ is the coefficient of friction and N is the normal force acting on the rope.
In this case, the normal force acting on the rope is equal to the weight of the rope that is hanging over the table, i.e.,
N = mgl1
The force balance equation in the horizontal direction is given by:
F2 - f = 0
mgsinθ - μN = 0
mgsinθ - μmgl1 = 0
l1 = sinθ/μ
Therefore, the maximum length of the rope that can overhang from the table without sliding down is given by:
l1 = l sinθ/μ
Substituting the given values, we get:
l1 = l/μ
Hence, the correct option is (c) l/μ.
Given:
- Length of rope = l
- Coefficient of friction =
To find:
- Maximum length of rope that can overhang from the table without sliding down.
Solution:
Let l1 be the maximum length of the rope that can overhang from the table without sliding down. We need to find the value of l1.
Consider the free body diagram of the rope as shown below:
The weight of the rope acts downward and can be resolved into two components:
- F1 = mgcosθ acts perpendicular to the table surface
- F2 = mgsinθ acts parallel to the table surface
The maximum value of friction force that can act on the rope is given by:
f = μN
where, μ is the coefficient of friction and N is the normal force acting on the rope.
In this case, the normal force acting on the rope is equal to the weight of the rope that is hanging over the table, i.e.,
N = mgl1
The force balance equation in the horizontal direction is given by:
F2 - f = 0
mgsinθ - μN = 0
mgsinθ - μmgl1 = 0
l1 = sinθ/μ
Therefore, the maximum length of the rope that can overhang from the table without sliding down is given by:
l1 = l sinθ/μ
Substituting the given values, we get:
l1 = l/μ
Hence, the correct option is (c) l/μ.
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A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer?.
A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer?.
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A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l1 of the part of this rope which can overhang from the edge of the table without sliding down is a)1/μb)1/μ+1c)μl/μ+1d)μl/μ-1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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