Moment of Inertia
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365938 A thin rod of length \(L\) and mass \(M\) is bent at its mid-point into two halves so that the angle between them is \(90^{\circ}\). The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod

1 \(\dfrac{M L^{2}}{6}\)
2 \(\dfrac{M L^{2}}{24}\)
3 \(\dfrac{\sqrt{2} M L^{2}}{24}\)
4 \(\dfrac{M L^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365939 A uniform thin bar of mass \(6\;\,m\) and length \(12\;L\) is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is

1 \(6 m L^{2}\)
2 \(20 m L^{2}\)
3 \(30 m L^{2}\)
4 \(\dfrac{12}{5} m L^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365940 If the moment of inertia of a disc about an axis tangential and parallel to its surface be \(I\), then what will be the moment of inertia about the axis tangential but perpendicular to the surface?

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

365941 A thin wire of length \(L\) and uniform linear mass density \(\rho\) is bent into a circular loop with centre at \(O\) as shown. The moment of inertia of the loop about an axis \(XY\) is
supporting img

1 \(\dfrac{3 \rho L^{3}}{8 \pi^{2}}\)
2 \(\dfrac{5 \rho L^{2}}{8 \pi^{2}}\)
3 \(\dfrac{\rho L^{2}}{16 \pi^{2}}\)
4 \(\dfrac{\rho L^{2}}{8 \pi^{2}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365942 Moment of inertia of uniform rod of mass \(m\) and length \(l\) is \(\dfrac{17}{12} m l^{2}\) about a line perpendicular to the rod. The distance of this line from the middle point of the rod is

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

365938 A thin rod of length \(L\) and mass \(M\) is bent at its mid-point into two halves so that the angle between them is \(90^{\circ}\). The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod

1 \(\dfrac{M L^{2}}{6}\)
2 \(\dfrac{M L^{2}}{24}\)
3 \(\dfrac{\sqrt{2} M L^{2}}{24}\)
4 \(\dfrac{M L^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365939 A uniform thin bar of mass \(6\;\,m\) and length \(12\;L\) is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is

1 \(6 m L^{2}\)
2 \(20 m L^{2}\)
3 \(30 m L^{2}\)
4 \(\dfrac{12}{5} m L^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365940 If the moment of inertia of a disc about an axis tangential and parallel to its surface be \(I\), then what will be the moment of inertia about the axis tangential but perpendicular to the surface?

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

365941 A thin wire of length \(L\) and uniform linear mass density \(\rho\) is bent into a circular loop with centre at \(O\) as shown. The moment of inertia of the loop about an axis \(XY\) is
supporting img

1 \(\dfrac{3 \rho L^{3}}{8 \pi^{2}}\)
2 \(\dfrac{5 \rho L^{2}}{8 \pi^{2}}\)
3 \(\dfrac{\rho L^{2}}{16 \pi^{2}}\)
4 \(\dfrac{\rho L^{2}}{8 \pi^{2}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365942 Moment of inertia of uniform rod of mass \(m\) and length \(l\) is \(\dfrac{17}{12} m l^{2}\) about a line perpendicular to the rod. The distance of this line from the middle point of the rod is

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

365938 A thin rod of length \(L\) and mass \(M\) is bent at its mid-point into two halves so that the angle between them is \(90^{\circ}\). The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod

1 \(\dfrac{M L^{2}}{6}\)
2 \(\dfrac{M L^{2}}{24}\)
3 \(\dfrac{\sqrt{2} M L^{2}}{24}\)
4 \(\dfrac{M L^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365939 A uniform thin bar of mass \(6\;\,m\) and length \(12\;L\) is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is

1 \(6 m L^{2}\)
2 \(20 m L^{2}\)
3 \(30 m L^{2}\)
4 \(\dfrac{12}{5} m L^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365940 If the moment of inertia of a disc about an axis tangential and parallel to its surface be \(I\), then what will be the moment of inertia about the axis tangential but perpendicular to the surface?

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

365941 A thin wire of length \(L\) and uniform linear mass density \(\rho\) is bent into a circular loop with centre at \(O\) as shown. The moment of inertia of the loop about an axis \(XY\) is
supporting img

1 \(\dfrac{3 \rho L^{3}}{8 \pi^{2}}\)
2 \(\dfrac{5 \rho L^{2}}{8 \pi^{2}}\)
3 \(\dfrac{\rho L^{2}}{16 \pi^{2}}\)
4 \(\dfrac{\rho L^{2}}{8 \pi^{2}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365942 Moment of inertia of uniform rod of mass \(m\) and length \(l\) is \(\dfrac{17}{12} m l^{2}\) about a line perpendicular to the rod. The distance of this line from the middle point of the rod is

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

365938 A thin rod of length \(L\) and mass \(M\) is bent at its mid-point into two halves so that the angle between them is \(90^{\circ}\). The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod

1 \(\dfrac{M L^{2}}{6}\)
2 \(\dfrac{M L^{2}}{24}\)
3 \(\dfrac{\sqrt{2} M L^{2}}{24}\)
4 \(\dfrac{M L^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365939 A uniform thin bar of mass \(6\;\,m\) and length \(12\;L\) is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is

1 \(6 m L^{2}\)
2 \(20 m L^{2}\)
3 \(30 m L^{2}\)
4 \(\dfrac{12}{5} m L^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365940 If the moment of inertia of a disc about an axis tangential and parallel to its surface be \(I\), then what will be the moment of inertia about the axis tangential but perpendicular to the surface?

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

365941 A thin wire of length \(L\) and uniform linear mass density \(\rho\) is bent into a circular loop with centre at \(O\) as shown. The moment of inertia of the loop about an axis \(XY\) is
supporting img

1 \(\dfrac{3 \rho L^{3}}{8 \pi^{2}}\)
2 \(\dfrac{5 \rho L^{2}}{8 \pi^{2}}\)
3 \(\dfrac{\rho L^{2}}{16 \pi^{2}}\)
4 \(\dfrac{\rho L^{2}}{8 \pi^{2}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365942 Moment of inertia of uniform rod of mass \(m\) and length \(l\) is \(\dfrac{17}{12} m l^{2}\) about a line perpendicular to the rod. The distance of this line from the middle point of the rod is

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

365938 A thin rod of length \(L\) and mass \(M\) is bent at its mid-point into two halves so that the angle between them is \(90^{\circ}\). The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod

1 \(\dfrac{M L^{2}}{6}\)
2 \(\dfrac{M L^{2}}{24}\)
3 \(\dfrac{\sqrt{2} M L^{2}}{24}\)
4 \(\dfrac{M L^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365939 A uniform thin bar of mass \(6\;\,m\) and length \(12\;L\) is bent to make a regular hexagon. Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is

1 \(6 m L^{2}\)
2 \(20 m L^{2}\)
3 \(30 m L^{2}\)
4 \(\dfrac{12}{5} m L^{2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365940 If the moment of inertia of a disc about an axis tangential and parallel to its surface be \(I\), then what will be the moment of inertia about the axis tangential but perpendicular to the surface?

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

365941 A thin wire of length \(L\) and uniform linear mass density \(\rho\) is bent into a circular loop with centre at \(O\) as shown. The moment of inertia of the loop about an axis \(XY\) is
supporting img

1 \(\dfrac{3 \rho L^{3}}{8 \pi^{2}}\)
2 \(\dfrac{5 \rho L^{2}}{8 \pi^{2}}\)
3 \(\dfrac{\rho L^{2}}{16 \pi^{2}}\)
4 \(\dfrac{\rho L^{2}}{8 \pi^{2}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365942 Moment of inertia of uniform rod of mass \(m\) and length \(l\) is \(\dfrac{17}{12} m l^{2}\) about a line perpendicular to the rod. The distance of this line from the middle point of the rod is

1 \(\dfrac{2}{3} l\)
2 \(\dfrac{l}{\sqrt{2}}\)
3 \(\dfrac{l}{2 \sqrt{3}}\)
4 \(\dfrac{2}{\sqrt{3}} l\)