Moment of Inertia
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365921 Moment of inertia of uniform triangular plate about axis passing through sides \(\mathrm{AB}, \mathrm{AC}\), and \(\mathrm{BC}\) are \(I_{P}, I_{B}\) and \(I_{H}\) respectively and about an axis perpendicular to the plane and passing through point \(\mathrm{C}\) is \(I_{C}\). Then:
supporting img

1 \(I_{P}>I_{H}>I_{B}>I_{C}\)
2 \(I_{C}>I_{P}>I_{B}>I_{H}\)
3 \(I_{H}>I_{B}>I_{C}>I_{P}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365922 Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is \(I\). If the same rod is bent into a ring and its moment of inertia about its diameter is \(I^{\prime}\), then the ratio \(\dfrac{I}{I^{\prime}}\) is

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

365923 Moment of inertia of a uniform circular disc about a diameter is \(I\). Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

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

365924 Two particles each mass \(m\), and other particle of mass \(2 m\) are situated at the verticles of an equilateral triangle \(A B C\) of side \(L\). What is the moment of inertia of the system about the line \(A X\) perpendicular to \(A B\) in the plane of \(A B C\) ?
supporting img

1 \(\frac{3}{2}\,m{L^2}\)
2 \(2\,m{L^2}\)
3 \(\frac{5}{4}\,m{L^2}\)
4 \(\frac{2}{3}\,m{L^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365925 The moment of inertia of a sphere (mass \(M\) and radius R) about it's diameter is \({\rm{I}}\). Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis \(X X^{\prime}\) will be :-
supporting img

1 \({\rm{5}}\,{\rm{ I}}\)
2 \({\rm{3}}\,{\rm{I}}\)
3 \({\rm{9}}\,{\rm{I}}\)
4 \({\rm{7}}\,{\rm{I}}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365921 Moment of inertia of uniform triangular plate about axis passing through sides \(\mathrm{AB}, \mathrm{AC}\), and \(\mathrm{BC}\) are \(I_{P}, I_{B}\) and \(I_{H}\) respectively and about an axis perpendicular to the plane and passing through point \(\mathrm{C}\) is \(I_{C}\). Then:
supporting img

1 \(I_{P}>I_{H}>I_{B}>I_{C}\)
2 \(I_{C}>I_{P}>I_{B}>I_{H}\)
3 \(I_{H}>I_{B}>I_{C}>I_{P}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365922 Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is \(I\). If the same rod is bent into a ring and its moment of inertia about its diameter is \(I^{\prime}\), then the ratio \(\dfrac{I}{I^{\prime}}\) is

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

365923 Moment of inertia of a uniform circular disc about a diameter is \(I\). Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

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

365924 Two particles each mass \(m\), and other particle of mass \(2 m\) are situated at the verticles of an equilateral triangle \(A B C\) of side \(L\). What is the moment of inertia of the system about the line \(A X\) perpendicular to \(A B\) in the plane of \(A B C\) ?
supporting img

1 \(\frac{3}{2}\,m{L^2}\)
2 \(2\,m{L^2}\)
3 \(\frac{5}{4}\,m{L^2}\)
4 \(\frac{2}{3}\,m{L^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365925 The moment of inertia of a sphere (mass \(M\) and radius R) about it's diameter is \({\rm{I}}\). Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis \(X X^{\prime}\) will be :-
supporting img

1 \({\rm{5}}\,{\rm{ I}}\)
2 \({\rm{3}}\,{\rm{I}}\)
3 \({\rm{9}}\,{\rm{I}}\)
4 \({\rm{7}}\,{\rm{I}}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365921 Moment of inertia of uniform triangular plate about axis passing through sides \(\mathrm{AB}, \mathrm{AC}\), and \(\mathrm{BC}\) are \(I_{P}, I_{B}\) and \(I_{H}\) respectively and about an axis perpendicular to the plane and passing through point \(\mathrm{C}\) is \(I_{C}\). Then:
supporting img

1 \(I_{P}>I_{H}>I_{B}>I_{C}\)
2 \(I_{C}>I_{P}>I_{B}>I_{H}\)
3 \(I_{H}>I_{B}>I_{C}>I_{P}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365922 Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is \(I\). If the same rod is bent into a ring and its moment of inertia about its diameter is \(I^{\prime}\), then the ratio \(\dfrac{I}{I^{\prime}}\) is

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

365923 Moment of inertia of a uniform circular disc about a diameter is \(I\). Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

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

365924 Two particles each mass \(m\), and other particle of mass \(2 m\) are situated at the verticles of an equilateral triangle \(A B C\) of side \(L\). What is the moment of inertia of the system about the line \(A X\) perpendicular to \(A B\) in the plane of \(A B C\) ?
supporting img

1 \(\frac{3}{2}\,m{L^2}\)
2 \(2\,m{L^2}\)
3 \(\frac{5}{4}\,m{L^2}\)
4 \(\frac{2}{3}\,m{L^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365925 The moment of inertia of a sphere (mass \(M\) and radius R) about it's diameter is \({\rm{I}}\). Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis \(X X^{\prime}\) will be :-
supporting img

1 \({\rm{5}}\,{\rm{ I}}\)
2 \({\rm{3}}\,{\rm{I}}\)
3 \({\rm{9}}\,{\rm{I}}\)
4 \({\rm{7}}\,{\rm{I}}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365921 Moment of inertia of uniform triangular plate about axis passing through sides \(\mathrm{AB}, \mathrm{AC}\), and \(\mathrm{BC}\) are \(I_{P}, I_{B}\) and \(I_{H}\) respectively and about an axis perpendicular to the plane and passing through point \(\mathrm{C}\) is \(I_{C}\). Then:
supporting img

1 \(I_{P}>I_{H}>I_{B}>I_{C}\)
2 \(I_{C}>I_{P}>I_{B}>I_{H}\)
3 \(I_{H}>I_{B}>I_{C}>I_{P}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365922 Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is \(I\). If the same rod is bent into a ring and its moment of inertia about its diameter is \(I^{\prime}\), then the ratio \(\dfrac{I}{I^{\prime}}\) is

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

365923 Moment of inertia of a uniform circular disc about a diameter is \(I\). Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

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

365924 Two particles each mass \(m\), and other particle of mass \(2 m\) are situated at the verticles of an equilateral triangle \(A B C\) of side \(L\). What is the moment of inertia of the system about the line \(A X\) perpendicular to \(A B\) in the plane of \(A B C\) ?
supporting img

1 \(\frac{3}{2}\,m{L^2}\)
2 \(2\,m{L^2}\)
3 \(\frac{5}{4}\,m{L^2}\)
4 \(\frac{2}{3}\,m{L^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365925 The moment of inertia of a sphere (mass \(M\) and radius R) about it's diameter is \({\rm{I}}\). Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis \(X X^{\prime}\) will be :-
supporting img

1 \({\rm{5}}\,{\rm{ I}}\)
2 \({\rm{3}}\,{\rm{I}}\)
3 \({\rm{9}}\,{\rm{I}}\)
4 \({\rm{7}}\,{\rm{I}}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365921 Moment of inertia of uniform triangular plate about axis passing through sides \(\mathrm{AB}, \mathrm{AC}\), and \(\mathrm{BC}\) are \(I_{P}, I_{B}\) and \(I_{H}\) respectively and about an axis perpendicular to the plane and passing through point \(\mathrm{C}\) is \(I_{C}\). Then:
supporting img

1 \(I_{P}>I_{H}>I_{B}>I_{C}\)
2 \(I_{C}>I_{P}>I_{B}>I_{H}\)
3 \(I_{H}>I_{B}>I_{C}>I_{P}\)
4 None of these
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365922 Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is \(I\). If the same rod is bent into a ring and its moment of inertia about its diameter is \(I^{\prime}\), then the ratio \(\dfrac{I}{I^{\prime}}\) is

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

365923 Moment of inertia of a uniform circular disc about a diameter is \(I\). Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

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

365924 Two particles each mass \(m\), and other particle of mass \(2 m\) are situated at the verticles of an equilateral triangle \(A B C\) of side \(L\). What is the moment of inertia of the system about the line \(A X\) perpendicular to \(A B\) in the plane of \(A B C\) ?
supporting img

1 \(\frac{3}{2}\,m{L^2}\)
2 \(2\,m{L^2}\)
3 \(\frac{5}{4}\,m{L^2}\)
4 \(\frac{2}{3}\,m{L^2}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365925 The moment of inertia of a sphere (mass \(M\) and radius R) about it's diameter is \({\rm{I}}\). Four such spheres are arranged as shown in the figure. The moment of inertia of the system about axis \(X X^{\prime}\) will be :-
supporting img

1 \({\rm{5}}\,{\rm{ I}}\)
2 \({\rm{3}}\,{\rm{I}}\)
3 \({\rm{9}}\,{\rm{I}}\)
4 \({\rm{7}}\,{\rm{I}}\)