Moment of Inertia
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365947 Four thin rods of same mass \(M\) and same length \(l\), from a square as shown in figure. Moment of inertia of this system about an axis through centre \(O\) and perpendicular to its plane is
supporting img

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

365948 A rod of length \(L\) is composed of a uniform length \(\dfrac{1}{2} L\) of wood whose mass is \(m_{w}\) and a uniform length \(\dfrac{1}{2} L\) of brass whose mass is \(m_{b}\). The moment of inertia I of the rod about an axis perpendicular to the rod and through its centre is equal to

1 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{2}\)
2 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{3}\)
3 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{12}\)
4 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{6}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365949 A thin rod of mass \({m}\) and length \({l}\) is bent into a
\({V}\)-shaped frame at its mid point as shown. The moment of inertia of the system about an axis passing through \(O\) perpendicular to the plane of the frame is equal to
supporting img

1 \({\dfrac{m l^{2}}{12}}\)
2 \({\dfrac{m l^{2}}{3}}\)
3 \({\dfrac{m l^{2}}{12} \sin ^{2} \theta}\)
4 \({\dfrac{1}{3} m l^{2} \sin \theta}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365950 For the given uniform square lamina \(A B C D\), whose centre is \(O\)
supporting img

1 \(I_{A C}=\sqrt{2} I_{E F}\)
2 \(I_{A C}=I_{E F}\)
3 \(I_{A D}=3 I_{E F}\)
4 \(\sqrt{2} I_{A C}=I_{E F}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365947 Four thin rods of same mass \(M\) and same length \(l\), from a square as shown in figure. Moment of inertia of this system about an axis through centre \(O\) and perpendicular to its plane is
supporting img

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

365948 A rod of length \(L\) is composed of a uniform length \(\dfrac{1}{2} L\) of wood whose mass is \(m_{w}\) and a uniform length \(\dfrac{1}{2} L\) of brass whose mass is \(m_{b}\). The moment of inertia I of the rod about an axis perpendicular to the rod and through its centre is equal to

1 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{2}\)
2 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{3}\)
3 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{12}\)
4 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{6}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365949 A thin rod of mass \({m}\) and length \({l}\) is bent into a
\({V}\)-shaped frame at its mid point as shown. The moment of inertia of the system about an axis passing through \(O\) perpendicular to the plane of the frame is equal to
supporting img

1 \({\dfrac{m l^{2}}{12}}\)
2 \({\dfrac{m l^{2}}{3}}\)
3 \({\dfrac{m l^{2}}{12} \sin ^{2} \theta}\)
4 \({\dfrac{1}{3} m l^{2} \sin \theta}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365950 For the given uniform square lamina \(A B C D\), whose centre is \(O\)
supporting img

1 \(I_{A C}=\sqrt{2} I_{E F}\)
2 \(I_{A C}=I_{E F}\)
3 \(I_{A D}=3 I_{E F}\)
4 \(\sqrt{2} I_{A C}=I_{E F}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365947 Four thin rods of same mass \(M\) and same length \(l\), from a square as shown in figure. Moment of inertia of this system about an axis through centre \(O\) and perpendicular to its plane is
supporting img

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

365948 A rod of length \(L\) is composed of a uniform length \(\dfrac{1}{2} L\) of wood whose mass is \(m_{w}\) and a uniform length \(\dfrac{1}{2} L\) of brass whose mass is \(m_{b}\). The moment of inertia I of the rod about an axis perpendicular to the rod and through its centre is equal to

1 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{2}\)
2 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{3}\)
3 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{12}\)
4 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{6}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365949 A thin rod of mass \({m}\) and length \({l}\) is bent into a
\({V}\)-shaped frame at its mid point as shown. The moment of inertia of the system about an axis passing through \(O\) perpendicular to the plane of the frame is equal to
supporting img

1 \({\dfrac{m l^{2}}{12}}\)
2 \({\dfrac{m l^{2}}{3}}\)
3 \({\dfrac{m l^{2}}{12} \sin ^{2} \theta}\)
4 \({\dfrac{1}{3} m l^{2} \sin \theta}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365950 For the given uniform square lamina \(A B C D\), whose centre is \(O\)
supporting img

1 \(I_{A C}=\sqrt{2} I_{E F}\)
2 \(I_{A C}=I_{E F}\)
3 \(I_{A D}=3 I_{E F}\)
4 \(\sqrt{2} I_{A C}=I_{E F}\)
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365947 Four thin rods of same mass \(M\) and same length \(l\), from a square as shown in figure. Moment of inertia of this system about an axis through centre \(O\) and perpendicular to its plane is
supporting img

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

365948 A rod of length \(L\) is composed of a uniform length \(\dfrac{1}{2} L\) of wood whose mass is \(m_{w}\) and a uniform length \(\dfrac{1}{2} L\) of brass whose mass is \(m_{b}\). The moment of inertia I of the rod about an axis perpendicular to the rod and through its centre is equal to

1 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{2}\)
2 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{3}\)
3 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{12}\)
4 \(\left(m_{w}+m_{b}\right) \dfrac{L^{2}}{6}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365949 A thin rod of mass \({m}\) and length \({l}\) is bent into a
\({V}\)-shaped frame at its mid point as shown. The moment of inertia of the system about an axis passing through \(O\) perpendicular to the plane of the frame is equal to
supporting img

1 \({\dfrac{m l^{2}}{12}}\)
2 \({\dfrac{m l^{2}}{3}}\)
3 \({\dfrac{m l^{2}}{12} \sin ^{2} \theta}\)
4 \({\dfrac{1}{3} m l^{2} \sin \theta}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

365950 For the given uniform square lamina \(A B C D\), whose centre is \(O\)
supporting img

1 \(I_{A C}=\sqrt{2} I_{E F}\)
2 \(I_{A C}=I_{E F}\)
3 \(I_{A D}=3 I_{E F}\)
4 \(\sqrt{2} I_{A C}=I_{E F}\)
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