Question

A sphere is rolling down an inclined plane without slipping. The ratio of rotational energy to total kinetic energy is

A. 5/7
B. 2/5
C. 2/7
D. none of these

Answer 1

The ratio of rotational energy to total kinetic energy for a sphere rolling down an inclined plane without slipping is 2/5 option B.

Step-by-step explanation:

When a sphere is rolling down an inclined plane without slipping, the ratio of rotational energy to total kinetic energy is given by the equation:

(1/2) × I × ω² / (1/2) × m × v²

Here, I is the moment of inertia of the sphere, ω is its angular velocity, m is its mass, and v is its linear velocity.

For a sphere rolling without slipping, the relationship between angular velocity and linear velocity is given by:

ω = v / R

where R is the radius of the sphere.

Substituting this relationship into the ratio equation gives:

(1/2) × (2/5) × (v² / R²) / (1/2) × m × v²

Simplifying further, we get:

2/5

So, the ratio of rotational energy to total kinetic energy for a sphere rolling down an inclined plane without slipping is 2/5.