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Work Done by Force of Gravity

A chain of ma...

Question

A chain of mass $m$ and length $l$ is placed on a table such that its $n$ th part is hanging. Find work done to take hanging part over the table

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Solution

Displacement of hanging part's $C O M = \frac{l}{2 n}$
mass of hanging part= $\frac{m}{n}$
$∴ ω = F_{S} cos θ ⟹ ω = F_{s}$ (as $θ = 0 °$ )
= $\frac{m}{m} g (\frac{l}{2 n})$
$ω = \frac{m g l}{2 n^{2}}$

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