Chain Challenge!

A chain of uniform density is piled up on the top of a table. A small hole is cut, through which the chain starts falling.The length of the entire chain is 1 m. Initially, one-third of the chain is hanging from the edge of the table.How long will it take the chain (in seconds) to slide off the table?

All collisions (between the links) are inelastic in nature, and energy is not conserved.

Details and Assumptions

\bullet The chain is not lying straight on the table. It is piled up on the table.

\bullet If you found any integral difficult then you may use WolframAlpha.

\bullet chain is inelastic in nature.

\bullet You may found this useful:

131xdxx3(133)=1.130\int _{ \frac { 1 }{ 3 } }^{ 1 }{ \frac { xdx }{ \sqrt { { x }^{ 3 }-\left( { \frac { 1 }{ 3 } }^{ 3 } \right) } } } =1.130

\bullet Take g=9.8m/s2g=9.8 m/s^{2}

Also try this.
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