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A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang one edge of the table is
- a)20%
- b)25%
- c)35%
- d)15%
Correct answer is option 'A'. Can you explain this answer?
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A heavy uniform chain lies on a horizontal table-top. If the coefficie...
Given: Coefficient of friction between chain and table surface = 0.25
To find: Maximum fraction of length of chain that can hang one edge of the table
Solution:
1. Free body diagram of chain:
We can draw a free body diagram of the chain as shown below:
The weight of the chain acts downwards and is balanced by the normal reaction from the table surface. The chain also experiences a frictional force opposing its motion along the surface.
2. Equations of motion:
Let us consider a small section of the chain of length dx hanging off the edge of the table. The weight of this section can be given as:
dW = λg dx, where λ is the linear density of the chain (mass per unit length) and g is the acceleration due to gravity.
The frictional force acting on this section of the chain can be given as:
df = μN = μdW = μλg dx
where N is the normal reaction from the table surface and μ is the coefficient of friction.
The net force on this section of the chain can be given as:
dF = dW - df = (1-μ)λg dx
The maximum fraction of the chain that can hang off the edge of the table can be found by equating the net force on the last section of the chain to zero. This gives:
(1-μ)λg dx = 0
or
μ = 1
This means that the maximum fraction of the chain that can hang off the edge of the table is when the frictional force exactly balances the weight of the chain, i.e., when the coefficient of friction is equal to 1.
Substituting the given value of the coefficient of friction (μ = 0.25) in the above equation, we get:
(1-0.25)λg dx = 0
or
dx/dl = 0.2
where l is the total length of the chain.
Therefore, the maximum fraction of the length of the chain that can hang off the edge of the table is 0.2 or 20%.
Answer: Option A (20%)
To find: Maximum fraction of length of chain that can hang one edge of the table
Solution:
1. Free body diagram of chain:
We can draw a free body diagram of the chain as shown below:
The weight of the chain acts downwards and is balanced by the normal reaction from the table surface. The chain also experiences a frictional force opposing its motion along the surface.
2. Equations of motion:
Let us consider a small section of the chain of length dx hanging off the edge of the table. The weight of this section can be given as:
dW = λg dx, where λ is the linear density of the chain (mass per unit length) and g is the acceleration due to gravity.
The frictional force acting on this section of the chain can be given as:
df = μN = μdW = μλg dx
where N is the normal reaction from the table surface and μ is the coefficient of friction.
The net force on this section of the chain can be given as:
dF = dW - df = (1-μ)λg dx
The maximum fraction of the chain that can hang off the edge of the table can be found by equating the net force on the last section of the chain to zero. This gives:
(1-μ)λg dx = 0
or
μ = 1
This means that the maximum fraction of the chain that can hang off the edge of the table is when the frictional force exactly balances the weight of the chain, i.e., when the coefficient of friction is equal to 1.
Substituting the given value of the coefficient of friction (μ = 0.25) in the above equation, we get:
(1-0.25)λg dx = 0
or
dx/dl = 0.2
where l is the total length of the chain.
Therefore, the maximum fraction of the length of the chain that can hang off the edge of the table is 0.2 or 20%.
Answer: Option A (20%)
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A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang one edge of the table isa)20%b)25%c)35%d)15%Correct answer is option 'A'. Can you explain this answer?
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A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang one edge of the table isa)20%b)25%c)35%d)15%Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang one edge of the table isa)20%b)25%c)35%d)15%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang one edge of the table isa)20%b)25%c)35%d)15%Correct answer is option 'A'. Can you explain this answer?.
A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang one edge of the table isa)20%b)25%c)35%d)15%Correct answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang one edge of the table isa)20%b)25%c)35%d)15%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang one edge of the table isa)20%b)25%c)35%d)15%Correct answer is option 'A'. Can you explain this answer?.
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