Final answer:
To find the acceleration of the hollow, spherical shell, analyze the forces acting on it. The parallel component of the gravitational force is responsible for the acceleration, and the friction force can be calculated as well.
Step-by-step explanation:
To find the acceleration of the hollow, spherical shell, we need to analyze the forces acting on it. Since the shell is rolling without slipping, there is static friction between the shell and the slope, which enables its motion. The gravitational force can be split into two components: the component parallel to the slope and the component perpendicular to the slope.
The parallel component of the gravitational force is responsible for the acceleration. We can calculate it using the equation:
f_parallel = m * g * sin(theta)
where m is the mass of the shell, g is the acceleration due to gravity, and theta is the angle of the slope. The friction force between the shell and the slope can be calculated using the equation:
friction_force = f_parallel - m * g * cos(theta)