Radius of Gyration

Q. Radius of gyration does not depend on

1. Shape and size of the body.
2. Position and configuration of axis of rotation.
3. Distribution of mass of the body with respect to axis of rotation.
4. Mass of the body.

Q. Find the radius of gyration of a uniform circular disc of radius $R=1\text{m}$ and mass $M=2\text{kg}$ about its axis passing through the edge and normal to the disc as shown in figure.

1. $\sqrt{\frac{1}{2}}\text{m}$
2. $\sqrt{\frac{5}{2}}\text{m}$
3. $1\text{m}$
4. $\sqrt{\frac{3}{2}}\text{m}$

Q. Find the radius of gyration of a uniform disc of radius $R$ and mass $M$ about its edge and perpendicular to the disc.

1. $\frac{\sqrt{5}}{2}R$
2. $\frac{3}{2}R$
3. $\sqrt{\frac{3}{2}}R$
4. $\frac{9}{2}R$

Q. Find the radius of gyration of a uniform circular disc of radius $R=1\text{m}$ and mass $M=2\text{kg}$ about its axis passing through the edge and normal to the disc as shown in figure.

1. $\sqrt{\frac{1}{2}}\text{m}$
2. $\sqrt{\frac{5}{2}}\text{m}$
3. $1\text{m}$
4. $\sqrt{\frac{3}{2}}\text{m}$

Q. Find the radius of gyration of a thin uniform rod of mass ${}^{\prime }{m}^{\prime }$ and length $l=9\text{m}$ about an axis passing through one end and perpendicular to the rod as shown in figure.

1. $\sqrt{3}\text{m}$
2. $2\sqrt{3}\text{m}$
3. $\frac{\sqrt{3}}{2}\text{m}$
4. $3\sqrt{3}\text{m}$

Q. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

1. $1:\sqrt{2}$
2. $1:3$
3. $2:1$
4. $\sqrt{5}:\sqrt{6}$

Q.

The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. Find the distance of the line from the centre.

1. $\sqrt{2}r$

2. $\frac{r}{\sqrt{2}}$

3. $2r$

4. $\frac{r}{2}$

Q. Two identical solid sphere each of mass $m=5\text{kg}$ and radius $r=1\text{m}$ are joined at the ends of a light rod of length $l=2\text{m}$ to form a system as shown in figure. Radius of gyration of the system about an axis perpendicular to the length of rod and passing through center of mass of system is

1. $\sqrt{44}\text{m}$
2. $\sqrt{2.4}\text{m}$
3. $\sqrt{3.2}\text{m}$
4. $\sqrt{4.4}\text{m}$

Q. Radius of gyration of a body about an axis$\left(I_A\right)$ is $5\text{m}$. Perpendicular distance of $\left(I_A\right)$ from center of mass of body is $3\text{m}$. Find its radius of gyration about an axis$\left(I_B\right)$ which is parallel to $\left(I_A\right)$ and also passing through center of mass of body.

1. $4\text{m}$
2. $5\text{m}$
3. $3\text{m}$
4. $6\text{m}$

Q. Find the ratio of radii of gyration of a circular disc and a circular ring of same mass and radius, about an axis passing through their centre and perpendicular to their planes.

1. $1:\sqrt{2}$
2. $3:2$
3. $2:1$
4. $\sqrt{2}:1$

Q. Find the radius of gyration of a thin uniform rod of mass ${}^{\prime }{m}^{\prime }$ and length $l=9\text{m}$ about an axis passing through one end and perpendicular to the rod as shown in figure.

1. $\sqrt{3}\text{m}$
2. $2\sqrt{3}\text{m}$
3. $\frac{\sqrt{3}}{2}\text{m}$
4. $3\sqrt{3}\text{m}$

Q. Find the ratio of radius of gyration about natural axis of a circular disk to that of a circular ring each having same mass and same radius.

1. $1:1$
2. $2:1$
3. $1:\sqrt{2}$
4. $\sqrt{2}:1$

Q. A circular disc of radius $2\text{m}$ has a hole of radius $1\text{m}$ at its centre. Then, find the radius of gyration of the disc about the axis passing through its centre and perpendicular to its plane. Given that mass per unit area of the disc varies as $\frac{{\sigma }_0}{r}$.

1. $\frac{\sqrt{21}}{3}\text{m}$
2. $\frac{\sqrt{31}}{3}\text{m}$
3. $\frac{\sqrt{20}}{3}\text{m}$
4. $\frac{\sqrt{41}}{3}\text{m}$