Question

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on:______.

a. the length of the incline.
b. the mass of the sphere.
c. the height of the incline.
d. the radius of the sphere.

Answer 1

C. The height of the incline.

Step-by-step explanation:

After modelling the sphere by using the Principle of Energy Conservation and Work-Energy Theorem, it is known that gravitational potential energy at the top of the incline is equal to the sum of a lesser gravitational potential energy and translational and rotational component of kinetic energy, which depends on angular velocity, at the bottom of the incline. The lower the height of the sphere, the greater the angular velocity. Likewise, the greater the height of the incline, the greater the maximum angular speed at the bottom.

Therefore, the correct answer is C.