A chain of mass m and length L is held on a frictionless table in such a way that 1nth part is hanging below the edge of table- Calculate the work done to pull the hanging part of the chain-

Length of chain hanging from the table =L4 Mass of chain of the hanging part =m4 Gravitational force on hanging part of the chain =mg4 Center of ...

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Standard XII

Physics

Distance

A chain of ma...

Question

A chain of mass $m$ and length $L$ is held on a frictionless table in such a way that $\frac{1}{n} t h$ part is hanging below the edge of table. Calculate the work done to pull the hanging part of the chain.

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Solution

Length of chain hanging from the table $= \frac{L}{4}$
Mass of chain of the hanging part $= \frac{m}{4}$
Gravitational force on hanging part of the chain $= \frac{m g}{4}$
Center of mass of the hanging part of the chain is at $\frac{L}{8}$ from the end (i.e. half of hanging length)
therefore,
Workdone $= F . s$
$= \frac{m g}{4} \times \frac{L}{8}$
$= \frac{m g L}{32}$
Hence, external workdone required to pull the hanging length of the chain $= \frac{1}{32} m g L$

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A chain of mass m and length L is held on a frictionless table in such a way that 1nth part is hanging below the edge of table. Calculate the work done to pull the hanging part of the chain.

A chain of mass $m$ and length $L$ is held on a frictionless table in such a way that $\frac{1}{n} t h$ part is hanging below the edge of table. Calculate the work done to pull the hanging part of the chain.