Medium
One quarter sector is cut from a uniform circular disc of radius $R$. This sector has mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is
- A$\frac{1}{2} M R^2$
- B$\frac{1}{4} M R^2$
- C$\frac{1}{8} M R^2$
- D$\sqrt{2} M R^2$
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Similar Questions
If $I_1$ is the moment of inertia of a thin rod of mass $M$ and length $l$ about an axis perpendicular to its length and passing through its centre of mass,and $I_2$ is the moment of inertia of the ring formed by bending the rod about an axis passing through its centre and perpendicular to its plane,then:
Difficult
View Solution$A$ disc of radius $R$ and thickness $\frac{R}{6}$ has moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. The disc is melted and recast into a solid sphere. The moment of inertia of the sphere about its diameter is
Match List-$I$ with List-$II$:
List-$I$ List-$II$ $(A)$ Moment of inertia of solid sphere of radius $R$ about any tangent $(I)$ $\frac{5}{3} MR^2$ $(B)$ Moment of inertia of hollow sphere of radius $R$ about any tangent $(II)$ $\frac{7}{5} MR^2$ $(C)$ Moment of inertia of circular ring of radius $R$ about its diameter $(III)$ $\frac{1}{4} MR^2$ $(D)$ Moment of inertia of circular disc of radius $R$ about any diameter $(IV)$ $\frac{1}{2} MR^2$
Choose the correct answer from the options given below:
| List-$I$ | List-$II$ |
| $(A)$ Moment of inertia of solid sphere of radius $R$ about any tangent | $(I)$ $\frac{5}{3} MR^2$ |
| $(B)$ Moment of inertia of hollow sphere of radius $R$ about any tangent | $(II)$ $\frac{7}{5} MR^2$ |
| $(C)$ Moment of inertia of circular ring of radius $R$ about its diameter | $(III)$ $\frac{1}{4} MR^2$ |
| $(D)$ Moment of inertia of circular disc of radius $R$ about any diameter | $(IV)$ $\frac{1}{2} MR^2$ |
Choose the correct answer from the options given below:
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:
Five particles of mass $2 \ kg$ each are attached to the rim of a circular disc of radius $0.1 \ m$ and negligible mass. The moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane is ........ $kg \ m^2$.
Medium
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