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A chain of mass m and length l is placed on a table with one-sixth of it hanging freely from the table
edge. The amount of work done to pull the chain on the table is-
edge. The amount of work done to pull the chain on the table is-
- a)mgl/4
- b)mgl/6
- c)mgl/72
- d)mgl/36
Correct answer is option 'C'. Can you explain this answer?
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To calculate the work done to pull the chain on the table, we need to consider the gravitational potential energy of the hanging part of the chain.
1. Analysis of the Situation:
- A chain of mass m and length l is placed on a table.
- One-sixth of the chain is hanging freely from the table edge.
- The chain is being pulled on the table.
2. Determining the Height of the Hanging Chain:
- As one-sixth of the chain is hanging freely, we can consider it as a separate object.
- The length of this hanging chain is (1/6) * l.
- To determine the height of this hanging chain, we need to calculate the vertical displacement of its center of mass from the table.
- The center of mass of the hanging chain is located at half of its length, which is (1/2) * (1/6) * l = (1/12) * l from the table.
- Therefore, the height of the hanging chain is (1/12) * l.
3. Calculating the Work Done:
- The work done to pull the chain on the table is equal to the change in gravitational potential energy.
- The change in potential energy is given by the formula: ΔPE = m * g * Δh, where m is the mass, g is the acceleration due to gravity, and Δh is the change in height.
- In this case, the mass of the hanging chain is (1/6) * m, and the change in height is (1/12) * l.
- Therefore, the work done is: ΔPE = (1/6) * m * g * (1/12) * l.
- Simplifying the expression, we get: ΔPE = (1/72) * m * g * l.
- Comparing this with the given options, we can see that the correct answer is option 'C': m * g * l / 72.
Thus, the amount of work done to pull the chain on the table is m * g * l / 72, as mentioned in option 'C'.
1. Analysis of the Situation:
- A chain of mass m and length l is placed on a table.
- One-sixth of the chain is hanging freely from the table edge.
- The chain is being pulled on the table.
2. Determining the Height of the Hanging Chain:
- As one-sixth of the chain is hanging freely, we can consider it as a separate object.
- The length of this hanging chain is (1/6) * l.
- To determine the height of this hanging chain, we need to calculate the vertical displacement of its center of mass from the table.
- The center of mass of the hanging chain is located at half of its length, which is (1/2) * (1/6) * l = (1/12) * l from the table.
- Therefore, the height of the hanging chain is (1/12) * l.
3. Calculating the Work Done:
- The work done to pull the chain on the table is equal to the change in gravitational potential energy.
- The change in potential energy is given by the formula: ΔPE = m * g * Δh, where m is the mass, g is the acceleration due to gravity, and Δh is the change in height.
- In this case, the mass of the hanging chain is (1/6) * m, and the change in height is (1/12) * l.
- Therefore, the work done is: ΔPE = (1/6) * m * g * (1/12) * l.
- Simplifying the expression, we get: ΔPE = (1/72) * m * g * l.
- Comparing this with the given options, we can see that the correct answer is option 'C': m * g * l / 72.
Thus, the amount of work done to pull the chain on the table is m * g * l / 72, as mentioned in option 'C'.
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A chain of mass m and length l is placed on a table with one-sixth of it hanging freely from the tableedge. The amount of work done to pull the chain on the table is-a)mgl/4b)mgl/6c)mgl/72d)mgl/36Correct answer is option 'C'. Can you explain this answer?
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