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:

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

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