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From a circular disc of radius $R$ and mass $9M$,a small disc of mass $M$ and radius $R/3$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is
- A$M R^2$
- B$\frac{40}{9} M R^2$
- C$4 M R^2$
- D$\frac{4}{9} M R^2$
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Similar Questions
The ratio of the radius of gyration of a circular disc to that of a circular ring,each of the same mass and radius,about their respective central axes is:
Three point masses,each of mass $m$,are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining the other two vertices is:
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:
The analogue of mass in rotational motion is:
Easy
View SolutionThree rods each of length $L$ and mass $M$ are placed along $X$,$Y$,and $Z$-axes in such a way that one end of each rod is at the origin. The moment of inertia of this system about the $Z$-axis is
Difficult
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