Question: A hollow sphere rolls down an incline. If its mass is m and radius is R, what is its moment of inertia?
Options:
(2/5)mR^2
(1/2)mR^2
(2/3)mR^2
(3/5)mR^2
Correct Answer: (2/3)mR^2
Solution:
The moment of inertia of a hollow sphere about its center is I = (2/3)mR^2.
A hollow sphere rolls down an incline. If its mass is m and radius is R, what is
Practice Questions
Q1
A hollow sphere rolls down an incline. If its mass is m and radius is R, what is its moment of inertia?
(2/5)mR^2
(1/2)mR^2
(2/3)mR^2
(3/5)mR^2
Questions & Step-by-Step Solutions
A hollow sphere rolls down an incline. If its mass is m and radius is R, what is its moment of inertia?
Step 1: Understand what a hollow sphere is. A hollow sphere is a spherical object that has a thin shell and is empty inside.
Step 2: Know that the moment of inertia is a measure of how difficult it is to change the rotation of an object.
Step 3: Identify the formula for the moment of inertia of a hollow sphere. The formula is I = (2/3)mR^2.
Step 4: Recognize that in the formula, 'm' represents the mass of the hollow sphere and 'R' represents its radius.
Step 5: Substitute the values of mass (m) and radius (R) into the formula if needed, but the general formula remains I = (2/3)mR^2.
Moment of Inertia – The moment of inertia quantifies how mass is distributed relative to an axis of rotation, affecting how easily an object can rotate.
Hollow Sphere Dynamics – Understanding the properties of hollow spheres, including their moment of inertia, is crucial for solving problems involving rotational motion.
Rolling Motion – The relationship between translational and rotational motion in rolling objects is essential for analyzing their dynamics on inclines.
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