A Ball in the Shape of a Uniform Spherical Shell $35 ^ { \circ }$

question 44

Essay

A ball in the shape of a uniform spherical shell (like a soccer ball) of mass 1.5 kg and
radius 15 cm rolls down a $35 ^ { \circ }$ incline that is 6.0 m high, measured vertically. The ball starts
from rest, and there is enough friction on the incline to prevent slipping of the ball.
(a) How fast is the ball moving forward when it reaches the bottom of the incline, and
what is its angular speed at that instant?
(b) If there were no friction on the incline, how fast would the ball be moving forward and
what would be its angular speed at the bottom?

---

Definitions:

Pure Competition

A market structure characterized by a large number of small firms, a homogeneous product, free entry and exit, and perfect information, leading to an efficient allocation of resources.

Four-Firm Concentration Ratios

A measure that assesses the total market share of the four largest firms within an industry, indicating the extent of market concentration.

Mutual Interdependence

A condition in which the actions or decisions of each firm in a market affect and are affected by those of other firms, particularly relevant in oligopolistic markets.

Localized Market

A market confined to a specific geographic area, where the products or services offered are tailored to the preferences of the local population.