A solid sphere rolls on a table without any slipping. What is the fraction of total K.E. associated with rotational K.E.?

Options

A. `2//7`
B. `2//5`
C. `3//5`
D. `5//7`

Explanation

To find the fraction of total kinetic energy associated with the rotational kinetic energy of a solid sphere rolling on a table without slipping, we can follow these steps:

### Step 1: Understand the Kinetic Energy Components
The total kinetic energy (K.E.) of a rolling solid sphere consists of two parts:
1. Translational K.E. (due to its linear motion)
2. Rotational K.E. (due to its rotation about its center of mass)

The formulas for these are:
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