A solid sphere rolls down an inclined plane and its velocity at the bottom is `v_(1)` .The same sphere slides down the plane (without friction ) and its velocity at the bottom is `v_(2)` . Find the relation between `v_(1) & v_(2)`

Explanation

To find the relationship between the velocities \( v_1 \) (the velocity of a solid sphere rolling down an inclined plane) and \( v_2 \) (the velocity of the same sphere sliding down the plane without friction), we can use the principles of energy conservation.

### Step-by-Step Solution:

1. **Identify the Potential Energy at the Top**:
The potential energy (PE) of the solid sphere at the height \( h \) is given by:
\[
PE = mgh
...