Moment of Inertia of Hollow Sphere

Q. Three identical spherical shells, each of mass $m$ and radius $r$ are placed as shown in figure. Consider an axis $X{X}^{\prime }$, which is touching two shells and passing through diameter of third shell. Moment of inertia of the system consisting of these three spherical shells about $X{X}^{\prime }$ axis is :

1. $\frac{11}{5}m{r}^2$
2. $4m{r}^2$
3. $\frac{16}{5}m{r}^2$
4. $3m{r}^2$

Q. The moment of inertia of a solid sphere of density $\rho$ and radius R about its diameter is

1. $\frac{105}{176}{R}^5\rho$
2. $\frac{105}{176}{R}^2\rho$
3. $\frac{176}{105}{R}^5\rho$
4. $\frac{176}{105}{R}^2\rho$

Q. From a solid sphere of mass M and radius R, a cube of maximum possible volume is cut. The moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

1. $\frac{M{R}^2}{32\sqrt{2}\pi }$
2. $\frac{M{R}^2}{16\sqrt{2}\pi }$
3. $\frac{4M{R}^2}{9\sqrt{3}\pi }$
4. $\frac{4M{R}^2}{3\sqrt{3}\pi }$

Q. In the figure shown below, a solid sphere of radius $5\text{m}$ is arranged concentrically with a hollow sphere of radius $9\text{m}$. Find the moment of inertia of the system about an axis passing through their centre. (Take $m_s=$ mass of solid sphere $=5\text{kg},m_h=$ mass of hollow sphere $=3\text{kg}$).

1. $202{\text{kg-m}}^2$
2. $212{\text{kg-m}}^2$
3. $162{\text{kg-m}}^2$
4. $81{\text{kg-m}}^2$

Q.

The moment of Inertia of a uniform hollow sphere of mass $M$ and radius $R$, about its diameter is $\frac{2}{3}M{R}^2$.

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1. False
2. True

Q.

Calculate the moment of Inertia of uniform solid sphere of mass $M$ and Radius $R$, about its diameter

1. $\frac{2}{3}M{R}^2$

2. $\frac{2}{5}M{R}^2$

3. $\frac{5}{3}M{R}^2$

4. $\frac{5}{2}M{R}^2$

Q. The moment of inertia of a solid sphere about an axis passing through its centre is $0.4{\text{kg-m}}^2$. If mass of the sphere is kept same, but its density is increased eight times, find the new moment of inertia of the sphere about the same axis.

1. ${\text{0.4 kg-m}}^2$
2. ${\text{0.1 kg-m}}^2$
3. ${\text{0.3 kg-m}}^2$
4. ${\text{0.2 kg-m}}^2$

Q. Two spheres each of mass $M$ and radius $\frac{R}{2}$ are connected with a massless rod of length $R$ as shown in the figure. The moment of inertia of the system about an axis $\left(Y{Y}^{\prime }\right)$ passing through the centre of one of the spheres and perpendicular to the rod is

1. $\frac{21}{5}M{R}^2$
2. $\frac{2}{5}M{R}^2$
3. $\frac{5}{2}M{R}^2$
4. $\frac{5}{21}M{R}^2$

Q. A hollow sphere of mass 50 kg and radius 5 cm is rotated about one of its diameter. The rotational inertia of hollow sphere about this axis is.

1. $2500kg{m}^2$
2. $\frac{2500}{3}kg{m}^2$
3. $\frac{2500}{3}kgc{m}^2$
4. $2500kgc{m}^2$