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A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is
- a)MgL
- b)MgL/3
- c)MgL/9
- d)MgL/18
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A uniform chain of length L and mass M is lying on a smooth table and ...
The hanging part of the chain which is to be pulled up can be considered as a point mass situated at the centre of the hanging part. The equivalent diagram is drawn.
Note : The work done in bringing the mass up will be equal to the change in potential energy of the mass.
Note : The work done in bringing the mass up will be equal to the change in potential energy of the mass.
W = Change in potential energy
Most Upvoted Answer
A uniform chain of length L and mass M is lying on a smooth table and ...
To understand why the correct answer is option 'D', let's break down the problem step by step.
1. Finding the mass of the hanging part:
- We are given that one third of the chain's length is hanging vertically down over the edge of the table.
- Since the chain is uniform, we can assume that the mass is distributed uniformly along its length.
- Therefore, the mass of the hanging part is (1/3) * M, where M is the total mass of the chain.
2. Finding the work required to lift the hanging part onto the table:
- When the hanging part is lifted onto the table, the height through which it is lifted is equal to the length of the hanging part.
- Let's denote the length of the hanging part as L/3, where L is the total length of the chain.
- The work done in lifting the hanging part is equal to the change in potential energy.
- The change in potential energy is given by the formula: ΔPE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height.
- Substituting the values we have, the work done is (1/3) * M * g * (L/3).
3. Simplifying the expression:
- We can simplify the expression further by canceling out common factors.
- (1/3) * M * g * (L/3) = M * g * (L/9).
Therefore, the work required to pull the hanging part onto the table is M * g * (L/9), which corresponds to option 'D'.
1. Finding the mass of the hanging part:
- We are given that one third of the chain's length is hanging vertically down over the edge of the table.
- Since the chain is uniform, we can assume that the mass is distributed uniformly along its length.
- Therefore, the mass of the hanging part is (1/3) * M, where M is the total mass of the chain.
2. Finding the work required to lift the hanging part onto the table:
- When the hanging part is lifted onto the table, the height through which it is lifted is equal to the length of the hanging part.
- Let's denote the length of the hanging part as L/3, where L is the total length of the chain.
- The work done in lifting the hanging part is equal to the change in potential energy.
- The change in potential energy is given by the formula: ΔPE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height.
- Substituting the values we have, the work done is (1/3) * M * g * (L/3).
3. Simplifying the expression:
- We can simplify the expression further by canceling out common factors.
- (1/3) * M * g * (L/3) = M * g * (L/9).
Therefore, the work required to pull the hanging part onto the table is M * g * (L/9), which corresponds to option 'D'.
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A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table isa)MgLb)MgL/3c)MgL/9d)MgL/18Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table isa)MgLb)MgL/3c)MgL/9d)MgL/18Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table isa)MgLb)MgL/3c)MgL/9d)MgL/18Correct answer is option 'D'. Can you explain this answer?.
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