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Question

A uniform chain of length l and mass m is placed on a smooth table with one-fourth of its length hanging over the edge. The work that has to be done to pull the whole chain back onto the table is?


A
14 mgl
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B
18 mgl
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C
116 mgl
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D
132 mgl
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Solution

The correct option is A $$\dfrac{1}{4}$$ mgl
$$W=\dfrac { M }{ L } dxg(x)$$
Total work done to pull the $$\dfrac { 1 }{ 4 } $$ part on the table
$$\int _{ 0 }^{ \dfrac { 1 }{ 4 }  }{ \dfrac { M }{ L }  } g(x)\quad dx$$
 $$\dfrac { M }{ L } g\int _{ 0 }^{ \dfrac { 1 }{ 4 }  }{ x\quad dx } =\dfrac { mgl }{ 4 } $$

Physics

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