If a solid sphere and a hollow sphere have the same mass and radius, which one w

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Question: If a solid sphere and a hollow sphere have the same mass and radius, which one will roll down an incline faster?

Options:

Correct Answer: Solid sphere

Solution:

The solid sphere will roll down the incline faster because it has a smaller moment of inertia compared to the hollow sphere.

If a solid sphere and a hollow sphere have the same mass and radius, which one will roll down an incline faster?

If a solid sphere and a hollow sphere have the same mass and radius, which one will roll down an incline faster?

Step 1: Understand that both spheres have the same mass and radius.
Step 2: Know that when objects roll down an incline, their shape affects how fast they roll.
Step 3: Learn about 'moment of inertia,' which is a measure of how difficult it is to change an object's rotation.
Step 4: Realize that a solid sphere has a smaller moment of inertia than a hollow sphere of the same mass and radius.
Step 5: Remember that a smaller moment of inertia means the object can roll down the incline faster.
Step 6: Conclude that the solid sphere will reach the bottom of the incline before the hollow sphere.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation. A lower moment of inertia allows an object to accelerate faster when rolling.
Rolling Motion – Rolling motion involves both translational and rotational motion, and the distribution of mass affects how quickly an object can roll down an incline.
Inclined Plane Dynamics – The dynamics of objects on an inclined plane involve gravitational force, friction, and the object's moment of inertia, which determines the acceleration down the slope.