Moment of Inertia
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365913 The ratio of radii of gyration of a ring to a disc ( both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

1 \(\dfrac{\sqrt{3}}{\sqrt{2}}\)
2 \(\dfrac{2}{\sqrt{5}}\)
3 \(\dfrac{\sqrt{2}}{1}\)
4 \(\dfrac{2}{\sqrt{3}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365914 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\dfrac{5}{6}}\)
2 \(\sqrt{\dfrac{5}{3}}\)
3 1
4 \(\dfrac{2}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365915 The moment of inertia of a circular disc of radius \(2\;m\) and mass \(1\;kg\) about an axis passing through the centre of mass but perpendicular to the plane of the disc is \(2\;kg\;{m^2}\). Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is____ (See the given figure).
supporting img

1 \(8\;kg\;{m^2}\)
2 \(4\;kg\;{m^2}\)
3 \(10\;kg\;{m^2}\)
4 \(6\;kg\;{m^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365916 \(A B C\) is right angled triangular plane of uniform thickness. The sides are such that \(A B>B C\) as shown in figure. \(I_{1}, I_{2}, I_{3}\) are moments of inertia about \(A B, B C\) and \(A C\), respectively. Then, which of the following relations is correct?
supporting img

1 \(I_{1}=I_{2}=I_{3}\)
2 \(I_{2}>I_{1}>I_{3}\)
3 \(I_{3} < I_{2} < I_{1}\)
4 \(I_{3}>I_{1}>I_{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365913 The ratio of radii of gyration of a ring to a disc ( both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

1 \(\dfrac{\sqrt{3}}{\sqrt{2}}\)
2 \(\dfrac{2}{\sqrt{5}}\)
3 \(\dfrac{\sqrt{2}}{1}\)
4 \(\dfrac{2}{\sqrt{3}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365914 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\dfrac{5}{6}}\)
2 \(\sqrt{\dfrac{5}{3}}\)
3 1
4 \(\dfrac{2}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365915 The moment of inertia of a circular disc of radius \(2\;m\) and mass \(1\;kg\) about an axis passing through the centre of mass but perpendicular to the plane of the disc is \(2\;kg\;{m^2}\). Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is____ (See the given figure).
supporting img

1 \(8\;kg\;{m^2}\)
2 \(4\;kg\;{m^2}\)
3 \(10\;kg\;{m^2}\)
4 \(6\;kg\;{m^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365916 \(A B C\) is right angled triangular plane of uniform thickness. The sides are such that \(A B>B C\) as shown in figure. \(I_{1}, I_{2}, I_{3}\) are moments of inertia about \(A B, B C\) and \(A C\), respectively. Then, which of the following relations is correct?
supporting img

1 \(I_{1}=I_{2}=I_{3}\)
2 \(I_{2}>I_{1}>I_{3}\)
3 \(I_{3} < I_{2} < I_{1}\)
4 \(I_{3}>I_{1}>I_{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365913 The ratio of radii of gyration of a ring to a disc ( both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

1 \(\dfrac{\sqrt{3}}{\sqrt{2}}\)
2 \(\dfrac{2}{\sqrt{5}}\)
3 \(\dfrac{\sqrt{2}}{1}\)
4 \(\dfrac{2}{\sqrt{3}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365914 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\dfrac{5}{6}}\)
2 \(\sqrt{\dfrac{5}{3}}\)
3 1
4 \(\dfrac{2}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365915 The moment of inertia of a circular disc of radius \(2\;m\) and mass \(1\;kg\) about an axis passing through the centre of mass but perpendicular to the plane of the disc is \(2\;kg\;{m^2}\). Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is____ (See the given figure).
supporting img

1 \(8\;kg\;{m^2}\)
2 \(4\;kg\;{m^2}\)
3 \(10\;kg\;{m^2}\)
4 \(6\;kg\;{m^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365916 \(A B C\) is right angled triangular plane of uniform thickness. The sides are such that \(A B>B C\) as shown in figure. \(I_{1}, I_{2}, I_{3}\) are moments of inertia about \(A B, B C\) and \(A C\), respectively. Then, which of the following relations is correct?
supporting img

1 \(I_{1}=I_{2}=I_{3}\)
2 \(I_{2}>I_{1}>I_{3}\)
3 \(I_{3} < I_{2} < I_{1}\)
4 \(I_{3}>I_{1}>I_{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365913 The ratio of radii of gyration of a ring to a disc ( both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

1 \(\dfrac{\sqrt{3}}{\sqrt{2}}\)
2 \(\dfrac{2}{\sqrt{5}}\)
3 \(\dfrac{\sqrt{2}}{1}\)
4 \(\dfrac{2}{\sqrt{3}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365914 Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

1 \(\sqrt{\dfrac{5}{6}}\)
2 \(\sqrt{\dfrac{5}{3}}\)
3 1
4 \(\dfrac{2}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365915 The moment of inertia of a circular disc of radius \(2\;m\) and mass \(1\;kg\) about an axis passing through the centre of mass but perpendicular to the plane of the disc is \(2\;kg\;{m^2}\). Its moment of inertia about an axis parallel to this axis but passing through the edge of the disc is____ (See the given figure).
supporting img

1 \(8\;kg\;{m^2}\)
2 \(4\;kg\;{m^2}\)
3 \(10\;kg\;{m^2}\)
4 \(6\;kg\;{m^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365916 \(A B C\) is right angled triangular plane of uniform thickness. The sides are such that \(A B>B C\) as shown in figure. \(I_{1}, I_{2}, I_{3}\) are moments of inertia about \(A B, B C\) and \(A C\), respectively. Then, which of the following relations is correct?
supporting img

1 \(I_{1}=I_{2}=I_{3}\)
2 \(I_{2}>I_{1}>I_{3}\)
3 \(I_{3} < I_{2} < I_{1}\)
4 \(I_{3}>I_{1}>I_{2}\)