269451
A wire of mass\(m\) and length \(l\) is bent in the form of circular ring. The moment of inertia of the ring about its axis is
1 \(m l^{2}\)
2 \(\frac{m l^{2}}{4 \pi^{2}}\)
3 \(\frac{m l^{2}}{2 \pi^{2}}\)
4 \(\frac{m l^{2}}{8 \pi^{2}}\)
Explanation:
\(I=m r^{2} ; r=\frac{l}{2 \pi}\)
Rotational Motion
269452
The moment of inertia of a thin uniform rod of mass \(M\) and length \(L\) about an axis perpendicular to the rod, through itscentre is I.The moment of inertia of the rod about an axis perpendicular to rod through its end point is
1 \(\frac{I}{4}\)
2 \(\frac{I}{2}\)
3 \(2 I\)
4 \(4 I\)
Explanation:
\(I=\frac{M L^{2}}{12} ; I=I_{C M}+M G \frac{L}{2} \theta^{2}\)
Rotational Motion
269453
Four point size bodies each of mass \(m\) are fixed at four corners of light square frame of side length \(1 \mathrm{~m}\). The radius of gyration of these four bodies about an axis perpendicular to the plane of frame passing through its centre is
1 \(\sqrt{2}\)
2 2
3 \(\frac{1}{\sqrt{2}}\)
4 \(\frac{1}{2}\)
Explanation:
\(I=2 m l^{2} ; k=\sqrt{\frac{I}{4 m}}\)
Rotational Motion
269454
Uniform square plate of mass 240 gramis made to rotate about an axis passing through any diagonal of plate. If its moment of inertia is \(2 \times 10^{-4} \mathrm{kgm}^{2}\) then its side length is
269451
A wire of mass\(m\) and length \(l\) is bent in the form of circular ring. The moment of inertia of the ring about its axis is
1 \(m l^{2}\)
2 \(\frac{m l^{2}}{4 \pi^{2}}\)
3 \(\frac{m l^{2}}{2 \pi^{2}}\)
4 \(\frac{m l^{2}}{8 \pi^{2}}\)
Explanation:
\(I=m r^{2} ; r=\frac{l}{2 \pi}\)
Rotational Motion
269452
The moment of inertia of a thin uniform rod of mass \(M\) and length \(L\) about an axis perpendicular to the rod, through itscentre is I.The moment of inertia of the rod about an axis perpendicular to rod through its end point is
1 \(\frac{I}{4}\)
2 \(\frac{I}{2}\)
3 \(2 I\)
4 \(4 I\)
Explanation:
\(I=\frac{M L^{2}}{12} ; I=I_{C M}+M G \frac{L}{2} \theta^{2}\)
Rotational Motion
269453
Four point size bodies each of mass \(m\) are fixed at four corners of light square frame of side length \(1 \mathrm{~m}\). The radius of gyration of these four bodies about an axis perpendicular to the plane of frame passing through its centre is
1 \(\sqrt{2}\)
2 2
3 \(\frac{1}{\sqrt{2}}\)
4 \(\frac{1}{2}\)
Explanation:
\(I=2 m l^{2} ; k=\sqrt{\frac{I}{4 m}}\)
Rotational Motion
269454
Uniform square plate of mass 240 gramis made to rotate about an axis passing through any diagonal of plate. If its moment of inertia is \(2 \times 10^{-4} \mathrm{kgm}^{2}\) then its side length is
269451
A wire of mass\(m\) and length \(l\) is bent in the form of circular ring. The moment of inertia of the ring about its axis is
1 \(m l^{2}\)
2 \(\frac{m l^{2}}{4 \pi^{2}}\)
3 \(\frac{m l^{2}}{2 \pi^{2}}\)
4 \(\frac{m l^{2}}{8 \pi^{2}}\)
Explanation:
\(I=m r^{2} ; r=\frac{l}{2 \pi}\)
Rotational Motion
269452
The moment of inertia of a thin uniform rod of mass \(M\) and length \(L\) about an axis perpendicular to the rod, through itscentre is I.The moment of inertia of the rod about an axis perpendicular to rod through its end point is
1 \(\frac{I}{4}\)
2 \(\frac{I}{2}\)
3 \(2 I\)
4 \(4 I\)
Explanation:
\(I=\frac{M L^{2}}{12} ; I=I_{C M}+M G \frac{L}{2} \theta^{2}\)
Rotational Motion
269453
Four point size bodies each of mass \(m\) are fixed at four corners of light square frame of side length \(1 \mathrm{~m}\). The radius of gyration of these four bodies about an axis perpendicular to the plane of frame passing through its centre is
1 \(\sqrt{2}\)
2 2
3 \(\frac{1}{\sqrt{2}}\)
4 \(\frac{1}{2}\)
Explanation:
\(I=2 m l^{2} ; k=\sqrt{\frac{I}{4 m}}\)
Rotational Motion
269454
Uniform square plate of mass 240 gramis made to rotate about an axis passing through any diagonal of plate. If its moment of inertia is \(2 \times 10^{-4} \mathrm{kgm}^{2}\) then its side length is
269451
A wire of mass\(m\) and length \(l\) is bent in the form of circular ring. The moment of inertia of the ring about its axis is
1 \(m l^{2}\)
2 \(\frac{m l^{2}}{4 \pi^{2}}\)
3 \(\frac{m l^{2}}{2 \pi^{2}}\)
4 \(\frac{m l^{2}}{8 \pi^{2}}\)
Explanation:
\(I=m r^{2} ; r=\frac{l}{2 \pi}\)
Rotational Motion
269452
The moment of inertia of a thin uniform rod of mass \(M\) and length \(L\) about an axis perpendicular to the rod, through itscentre is I.The moment of inertia of the rod about an axis perpendicular to rod through its end point is
1 \(\frac{I}{4}\)
2 \(\frac{I}{2}\)
3 \(2 I\)
4 \(4 I\)
Explanation:
\(I=\frac{M L^{2}}{12} ; I=I_{C M}+M G \frac{L}{2} \theta^{2}\)
Rotational Motion
269453
Four point size bodies each of mass \(m\) are fixed at four corners of light square frame of side length \(1 \mathrm{~m}\). The radius of gyration of these four bodies about an axis perpendicular to the plane of frame passing through its centre is
1 \(\sqrt{2}\)
2 2
3 \(\frac{1}{\sqrt{2}}\)
4 \(\frac{1}{2}\)
Explanation:
\(I=2 m l^{2} ; k=\sqrt{\frac{I}{4 m}}\)
Rotational Motion
269454
Uniform square plate of mass 240 gramis made to rotate about an axis passing through any diagonal of plate. If its moment of inertia is \(2 \times 10^{-4} \mathrm{kgm}^{2}\) then its side length is
