A uniform chain of length l and mass m overhangs a smooth table with its two third part lying on the table. Find the kinetic energy of the chain as it completely slips off the table.

Explanation

To solve the problem of finding the kinetic energy of a uniform chain of length \( l \) and mass \( m \) as it completely slips off a smooth table, we can follow these steps:

### Step 1: Understand the Configuration of the Chain
- The chain has a total length \( l \).
- Two-thirds of the chain, which is \( \frac{2l}{3} \), is on the table, and one-third, which is \( \frac{l}{3} \), is hanging off the edge.

### Step 2: Determine the Initial Potential Energy
- The center of mass of the hanging part (length \( \frac{l}{3} \)) is at a height of \( \frac{l}{6} \) below the table.
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