A uniform chain of length l and mass m lies on a smooth table. A very small part of this chain hangs from the table. It begins to fall under the weight of hanging part. Find the velocity of chain when the length of hanging part becomes y.

Explanation

To solve the problem of finding the velocity of a uniform chain when a portion of it hangs off a smooth table, we can use the principles of energy conservation. Here's a step-by-step breakdown of the solution:

### Step 1: Define the Variables
- Let the total length of the chain be \( L \).
- Let the mass of the chain be \( m \).
- The mass per unit length (linear density) of the chain is given by:
\[
\lambda = \frac{m}{L}
...