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A uniform chain of length 2 m is kept on a table, such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?
- a)3.6 J
- b)7.2 J
- c)120 J
- d)1200 J
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A uniform chain of length 2 m is kept on a table, such that a length o...
Given:
Length of chain = 2 m
Length of hanging chain = 60 cm = 0.6 m
Total mass of chain = 4 kg
To find:
Work done in pulling the entire chain on the table
Solution:
1. Finding the mass of the hanging chain
Mass of the hanging chain can be found using the formula:
m = (length of hanging chain / total length of chain) x total mass of chain
m = (0.6 / 2) x 4
m = 1.2 kg
2. Finding the work done in pulling the hanging chain
Work done in pulling the hanging chain can be found using the formula:
W = mgh
Where,
m = mass of the hanging chain = 1.2 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height from which the chain is hanging = 0.6 m
W = 1.2 x 9.8 x 0.6
W = 7.056 J
3. Finding the work done in pulling the remaining chain
The remaining chain has a mass of 2.8 kg (total mass of chain - mass of hanging chain).
To lift the remaining chain, work is done against the force of gravity.
Work done in lifting the remaining chain can be found using the formula:
W = mgh
Where,
m = mass of the remaining chain = 2.8 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height to which the chain is lifted = 1.4 m (the total length of the chain minus the length of the hanging chain)
W = 2.8 x 9.8 x 1.4
W = 38.864 J
4. Finding the total work done
The total work done in pulling the entire chain on the table is the sum of the work done in pulling the hanging chain and the work done in pulling the remaining chain.
Total work done = work done in pulling the hanging chain + work done in pulling the remaining chain
Total work done = 7.056 + 38.864
Total work done = 45.92 J
Rounding off to one decimal place, we get:
Total work done = 45.9 J
Therefore, the correct option is A) 3.6 J.
Note: The correct answer is not A) 3.6 J. There seems to be an error in the answer key. The correct answer is 45.9 J.
Length of chain = 2 m
Length of hanging chain = 60 cm = 0.6 m
Total mass of chain = 4 kg
To find:
Work done in pulling the entire chain on the table
Solution:
1. Finding the mass of the hanging chain
Mass of the hanging chain can be found using the formula:
m = (length of hanging chain / total length of chain) x total mass of chain
m = (0.6 / 2) x 4
m = 1.2 kg
2. Finding the work done in pulling the hanging chain
Work done in pulling the hanging chain can be found using the formula:
W = mgh
Where,
m = mass of the hanging chain = 1.2 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height from which the chain is hanging = 0.6 m
W = 1.2 x 9.8 x 0.6
W = 7.056 J
3. Finding the work done in pulling the remaining chain
The remaining chain has a mass of 2.8 kg (total mass of chain - mass of hanging chain).
To lift the remaining chain, work is done against the force of gravity.
Work done in lifting the remaining chain can be found using the formula:
W = mgh
Where,
m = mass of the remaining chain = 2.8 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height to which the chain is lifted = 1.4 m (the total length of the chain minus the length of the hanging chain)
W = 2.8 x 9.8 x 1.4
W = 38.864 J
4. Finding the total work done
The total work done in pulling the entire chain on the table is the sum of the work done in pulling the hanging chain and the work done in pulling the remaining chain.
Total work done = work done in pulling the hanging chain + work done in pulling the remaining chain
Total work done = 7.056 + 38.864
Total work done = 45.92 J
Rounding off to one decimal place, we get:
Total work done = 45.9 J
Therefore, the correct option is A) 3.6 J.
Note: The correct answer is not A) 3.6 J. There seems to be an error in the answer key. The correct answer is 45.9 J.
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Community Answer
A uniform chain of length 2 m is kept on a table, such that a length o...
As the mass is uniformly distributed over length let us define mass per unit length as d = M/L = 4/2 = 2 kg/m
Length of hanging portion = 60 cm = 0.6 m
Mass of the hanging portion = m = d x 0.6 = 1.2 Kg
As we are dealing with mass distributions (here chain) and not particle it is better to consider centre of mass to solve the problem. Although 0.6 m chain is hanging the center of mass is at 0.3 m. So, we must only pull 0.3 m part of the string. Also, we are doing work against weight of the chain (mg).
W = F x S = mg x (0.3)
W = 1.2 x 10 x 0.3
W = 3.6 J
Length of hanging portion = 60 cm = 0.6 m
Mass of the hanging portion = m = d x 0.6 = 1.2 Kg
As we are dealing with mass distributions (here chain) and not particle it is better to consider centre of mass to solve the problem. Although 0.6 m chain is hanging the center of mass is at 0.3 m. So, we must only pull 0.3 m part of the string. Also, we are doing work against weight of the chain (mg).
W = F x S = mg x (0.3)
W = 1.2 x 10 x 0.3
W = 3.6 J
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A uniform chain of length 2 m is kept on a table, such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?a)3.6 Jb)7.2 Jc)120 Jd)1200 JCorrect answer is option 'A'. Can you explain this answer?
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