Moment of Inertia
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365951 The moment of inertia of a thin uniform rod of mass \(M\) and lenght \(L\) about an axis passing through its mid-point and perpendicular to its length is \(I_{0}\). Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

1 \(I_{0}+M L^{2} / 4\)
2 \(I_{0}+2 M L^{2}\)
3 \(I_{0}+M L^{2}\)
4 \(I_{0}+M L^{2} / 2\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365952 A solid cylinder has mass \(M\), radius \(R\) and length \(l\). Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is

1 \(\dfrac{2 M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
2 \(\dfrac{M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
3 \(\dfrac{3 M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
4 \(\dfrac{M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365953 The moment of inertia of a sphere of mass \(M\) and radius \(\mathrm{R}\) about an axis passing through its centre is \((2 / 5) M R^{2}\). The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

1 \(\dfrac{7}{5} R\)
2 \(\dfrac{3}{5} R\)
3 \(\left(\sqrt{\dfrac{7}{5}}\right) R\)
4 \(\left(\sqrt{\dfrac{3}{5}}\right) R\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365954 The moment of inertia of a door of mass \(m\), length \(2 l\) and width \(l\) about its longer side is

1 \(\dfrac{5 m l^{2}}{24}\)
2 \(\dfrac{m l^{2}}{3}\)
3 \(\dfrac{11 m l^{2}}{3}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365955 Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of inertia about their diameter axis \(A B\) as shown in figure is \(\sqrt{\dfrac{8}{x}}\). The value of \(x\) is
supporting img

1 17
2 51
3 34
4 67
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365951 The moment of inertia of a thin uniform rod of mass \(M\) and lenght \(L\) about an axis passing through its mid-point and perpendicular to its length is \(I_{0}\). Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

1 \(I_{0}+M L^{2} / 4\)
2 \(I_{0}+2 M L^{2}\)
3 \(I_{0}+M L^{2}\)
4 \(I_{0}+M L^{2} / 2\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365952 A solid cylinder has mass \(M\), radius \(R\) and length \(l\). Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is

1 \(\dfrac{2 M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
2 \(\dfrac{M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
3 \(\dfrac{3 M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
4 \(\dfrac{M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365953 The moment of inertia of a sphere of mass \(M\) and radius \(\mathrm{R}\) about an axis passing through its centre is \((2 / 5) M R^{2}\). The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

1 \(\dfrac{7}{5} R\)
2 \(\dfrac{3}{5} R\)
3 \(\left(\sqrt{\dfrac{7}{5}}\right) R\)
4 \(\left(\sqrt{\dfrac{3}{5}}\right) R\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365954 The moment of inertia of a door of mass \(m\), length \(2 l\) and width \(l\) about its longer side is

1 \(\dfrac{5 m l^{2}}{24}\)
2 \(\dfrac{m l^{2}}{3}\)
3 \(\dfrac{11 m l^{2}}{3}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365955 Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of inertia about their diameter axis \(A B\) as shown in figure is \(\sqrt{\dfrac{8}{x}}\). The value of \(x\) is
supporting img

1 17
2 51
3 34
4 67
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365951 The moment of inertia of a thin uniform rod of mass \(M\) and lenght \(L\) about an axis passing through its mid-point and perpendicular to its length is \(I_{0}\). Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

1 \(I_{0}+M L^{2} / 4\)
2 \(I_{0}+2 M L^{2}\)
3 \(I_{0}+M L^{2}\)
4 \(I_{0}+M L^{2} / 2\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365952 A solid cylinder has mass \(M\), radius \(R\) and length \(l\). Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is

1 \(\dfrac{2 M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
2 \(\dfrac{M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
3 \(\dfrac{3 M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
4 \(\dfrac{M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365953 The moment of inertia of a sphere of mass \(M\) and radius \(\mathrm{R}\) about an axis passing through its centre is \((2 / 5) M R^{2}\). The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

1 \(\dfrac{7}{5} R\)
2 \(\dfrac{3}{5} R\)
3 \(\left(\sqrt{\dfrac{7}{5}}\right) R\)
4 \(\left(\sqrt{\dfrac{3}{5}}\right) R\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365954 The moment of inertia of a door of mass \(m\), length \(2 l\) and width \(l\) about its longer side is

1 \(\dfrac{5 m l^{2}}{24}\)
2 \(\dfrac{m l^{2}}{3}\)
3 \(\dfrac{11 m l^{2}}{3}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365955 Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of inertia about their diameter axis \(A B\) as shown in figure is \(\sqrt{\dfrac{8}{x}}\). The value of \(x\) is
supporting img

1 17
2 51
3 34
4 67
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365951 The moment of inertia of a thin uniform rod of mass \(M\) and lenght \(L\) about an axis passing through its mid-point and perpendicular to its length is \(I_{0}\). Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

1 \(I_{0}+M L^{2} / 4\)
2 \(I_{0}+2 M L^{2}\)
3 \(I_{0}+M L^{2}\)
4 \(I_{0}+M L^{2} / 2\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365952 A solid cylinder has mass \(M\), radius \(R\) and length \(l\). Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is

1 \(\dfrac{2 M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
2 \(\dfrac{M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
3 \(\dfrac{3 M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
4 \(\dfrac{M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365953 The moment of inertia of a sphere of mass \(M\) and radius \(\mathrm{R}\) about an axis passing through its centre is \((2 / 5) M R^{2}\). The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

1 \(\dfrac{7}{5} R\)
2 \(\dfrac{3}{5} R\)
3 \(\left(\sqrt{\dfrac{7}{5}}\right) R\)
4 \(\left(\sqrt{\dfrac{3}{5}}\right) R\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365954 The moment of inertia of a door of mass \(m\), length \(2 l\) and width \(l\) about its longer side is

1 \(\dfrac{5 m l^{2}}{24}\)
2 \(\dfrac{m l^{2}}{3}\)
3 \(\dfrac{11 m l^{2}}{3}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365955 Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of inertia about their diameter axis \(A B\) as shown in figure is \(\sqrt{\dfrac{8}{x}}\). The value of \(x\) is
supporting img

1 17
2 51
3 34
4 67
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365951 The moment of inertia of a thin uniform rod of mass \(M\) and lenght \(L\) about an axis passing through its mid-point and perpendicular to its length is \(I_{0}\). Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is

1 \(I_{0}+M L^{2} / 4\)
2 \(I_{0}+2 M L^{2}\)
3 \(I_{0}+M L^{2}\)
4 \(I_{0}+M L^{2} / 2\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365952 A solid cylinder has mass \(M\), radius \(R\) and length \(l\). Its moment of inertia about an axis passing through its centre and perpendicular to its own axis is

1 \(\dfrac{2 M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
2 \(\dfrac{M R^{2}}{3}+\dfrac{M l^{2}}{12}\)
3 \(\dfrac{3 M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
4 \(\dfrac{M R^{2}}{4}+\dfrac{M l^{2}}{12}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365953 The moment of inertia of a sphere of mass \(M\) and radius \(\mathrm{R}\) about an axis passing through its centre is \((2 / 5) M R^{2}\). The radius of gyration of the sphere about a parallel axis to the above and tangent to the sphere is

1 \(\dfrac{7}{5} R\)
2 \(\dfrac{3}{5} R\)
3 \(\left(\sqrt{\dfrac{7}{5}}\right) R\)
4 \(\left(\sqrt{\dfrac{3}{5}}\right) R\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365954 The moment of inertia of a door of mass \(m\), length \(2 l\) and width \(l\) about its longer side is

1 \(\dfrac{5 m l^{2}}{24}\)
2 \(\dfrac{m l^{2}}{3}\)
3 \(\dfrac{11 m l^{2}}{3}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365955 Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of inertia about their diameter axis \(A B\) as shown in figure is \(\sqrt{\dfrac{8}{x}}\). The value of \(x\) is
supporting img

1 17
2 51
3 34
4 67