Question:
$I_S$ and $I_H$ are the moments of inertia about the diameters of a solid and thin walled hollow sphere respectively. If the radii and the masses of the above spheres are equal, $I_H > I_S$.
In solid sphere, the mass is continuously and regularly distributed about the centre whereas the mass, to a large extent, is concentrated on the surface of hollow sphere
$I_S$ and $I_H$ are the moments of inertia about the diameters of a solid and thin walled hollow sphere respectively. If the radii and the masses of the above spheres are equal, $I_H > I_S$.
In solid sphere, the mass is continuously and regularly distributed about the centre whereas the mass, to a large extent, is concentrated on the surface of hollow sphere
Updated On: May 21, 2024
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Solution and Explanation
The moment of inertia of solid sphere about its diameter
$I_S=\frac{2}{3}MR^2$
The moment of inertia of a thin walled hollow sphere about its diameter is
$I_H=\frac{2}{5}M\frac{(R^5_2-R^5_1)}{(R^3_2-R^3_1)}$ where $R_1 \,and \,R_2$ are its internal and external radii
= $I_H >I_s$
The reason is that in solid sphere the whole mass is uniformly and continuously distributed about its center in the whole volume while in hollow sphere the mass is distributed on the surface of sphere
$I_S=\frac{2}{3}MR^2$
The moment of inertia of a thin walled hollow sphere about its diameter is
$I_H=\frac{2}{5}M\frac{(R^5_2-R^5_1)}{(R^3_2-R^3_1)}$ where $R_1 \,and \,R_2$ are its internal and external radii
= $I_H >I_s$
The reason is that in solid sphere the whole mass is uniformly and continuously distributed about its center in the whole volume while in hollow sphere the mass is distributed on the surface of sphere
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.