A solid sphere of mass \(2m\) and a thin hollow spherical shell of mass \(m\) both roll down an inclined plane. What is the relationship between their accelerations?

A. The acceleration of the solid sphere is twice that of the hollow shell.
B. The acceleration of the hollow shell is twice that of the solid sphere.
C. The accelerations are equal.
D. The relationship cannot be determined without additional information.

Question

13-12-2023
Physics

High School

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A solid sphere of mass \(2m\) and a thin hollow spherical shell of mass \(m\) both roll down an inclined plane. What is the relationship between their accelerations?

A. The acceleration of the solid sphere is twice that of the hollow shell.
B. The acceleration of the hollow shell is twice that of the solid sphere.
C. The accelerations are equal.
D. The relationship cannot be determined without additional information.

Answer :

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Final answer:

The accelerations of a solid sphere and a thin hollow spherical shell are equal. The correct option is C.

Explanation:

The relationship between the accelerations of a solid sphere and a thin hollow spherical shell is that they are equal, or option c. the accelerations are equal. The acceleration of an object rolling down an incline is determined by the moment of inertia and the rotational kinetic energy.

For a solid sphere, both the moment of inertia and the rotational kinetic energy depend on the mass and radius of the sphere. As both the solid sphere and the hollow spherical shell have the same mass and radius, their moment of inertia and rotational kinetic energy will be the same. Therefore, their accelerations will also be the same.

An example that illustrates this relationship is when a solid sphere and a hollow spherical shell with the same mass and radius are released from the same height on an incline. Both objects will accelerate at the same rate and reach the bottom of the incline at the same time.