Easy
What are the factors on which the magnitude of the moment of inertia depends?
(N/A) The moment of inertia $(I)$ of a rigid body depends on the following factors:
$1$. Mass of the body: The moment of inertia is directly proportional to the mass of the body.
$2$. Distribution of mass: It depends on how the mass is distributed relative to the axis of rotation. If more mass is concentrated farther from the axis,the moment of inertia increases.
$3$. Position and orientation of the axis of rotation: The moment of inertia changes if the axis of rotation is shifted or its orientation is changed relative to the body.
$1$. Mass of the body: The moment of inertia is directly proportional to the mass of the body.
$2$. Distribution of mass: It depends on how the mass is distributed relative to the axis of rotation. If more mass is concentrated farther from the axis,the moment of inertia increases.
$3$. Position and orientation of the axis of rotation: The moment of inertia changes if the axis of rotation is shifted or its orientation is changed relative to the body.
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View SolutionThe ratio of the radius of gyration of a hollow sphere to that of a solid cylinder of equal mass,for the moment of inertia about their diameter axis $AB$ as shown in the figure,is $\sqrt{\frac{8}{x}}$. The value of $x$ is:
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View Solution List-$I$ List-$II$ $(a)$ $MI$ of the rod (length $L$,mass $M$,about an axis $\perp$ to the rod passing through the midpoint) $(i) \frac{8ML^2}{3}$ $(b)$ $MI$ of the rod (length $L$,mass $2M$,about an axis $\perp$ to the rod passing through one of its ends) $(ii) \frac{ML^2}{3}$ $(c)$ $MI$ of the rod (length $2L$,mass $M$,about an axis $\perp$ to the rod passing through its midpoint) $(iii) \frac{ML^2}{12}$ $(d)$ $MI$ of the rod (length $2L$,mass $2M$,about an axis $\perp$ to the rod passing through one of its ends) $(iv) \frac{2ML^2}{3}$
Choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
|---|---|
| $(a)$ $MI$ of the rod (length $L$,mass $M$,about an axis $\perp$ to the rod passing through the midpoint) | $(i) \frac{8ML^2}{3}$ |
| $(b)$ $MI$ of the rod (length $L$,mass $2M$,about an axis $\perp$ to the rod passing through one of its ends) | $(ii) \frac{ML^2}{3}$ |
| $(c)$ $MI$ of the rod (length $2L$,mass $M$,about an axis $\perp$ to the rod passing through its midpoint) | $(iii) \frac{ML^2}{12}$ |
| $(d)$ $MI$ of the rod (length $2L$,mass $2M$,about an axis $\perp$ to the rod passing through one of its ends) | $(iv) \frac{2ML^2}{3}$ |
Choose the correct answer from the options given below:
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