A table with smooth horizontal surface is turning at an angular speed `omega` about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance a from the centre. Find the speed of the speed of the particle as its distance from teh centre becomes L.

Explanation

To solve the problem, we need to find the speed of a particle placed in a groove on a rotating table as its distance from the center changes from \( a \) to \( L \). We will use the principles of circular motion and calculus to derive the speed.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The table is rotating with a constant angular speed \( \omega \).
- A particle is placed at a distance \( a \) from the center of the table in a groove that allows it to move radially outward.

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