269576
If \(I_{1}\) is moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre and \(I_{2}\) is its moment of inertia when it is bent into a shape of a ring then (Axis passing through its centre and perpendicular to its plane)
269577
The moment of inertia of thin rod of linear density \(\lambda\) and length \(I\) about an axis passing through one end and perpendicular to its length is
269578
Moment of inertia of a bar magnet of mass \(M\), length \(L\) and breadth \(B\) is \(I\). Then moment of inertia of another bar magnet with all these values doubled would be
1 \(8 \mathrm{I}\)
2 \(4 \mathrm{I}\)
3 \(2 I\)
4 I
Explanation:
\(I=\frac{M}{12}\left(L^{2}+b^{2}\right) \quad\)
Rotational Motion
269621
A square plate of mass \(M\) and edge \(L\) is shown in figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle \(15^{\circ}\) with the horizontal is
1 \(\frac{M L^{2}}{12}\)
2 \(\frac{11 M L^{2}}{24}\)
3 \(\frac{7 M L^{2}}{12}\)
4 \(\frac{10 M L^{2}}{24}\)
Explanation:
From diagram, we get \(x=A O \sin 60^{\circ}\)
\(=\frac{L}{\sqrt{2}} \times \frac{\sqrt{3}}{2} ; I_{z}=\frac{M L^{2}}{6} ; I_{x}=I_{y}=\frac{M L^{2}}{12}\)
\(I_{A B}=\frac{M L^{2}}{12}+M x^{2}\)
Rotational Motion
269622
A thin rod of length \(L\) and mass \(M\) is bent at the middle point \(O\) at an angle of \(60^{\circ}\). The moment of inertia of the rod about an axis passing through \(O\) and perpendicular to the plane of the rod will be
1 \(\frac{M L^{2}}{6}\)
2 \(\frac{M L^{2}}{12}\)
3 \(\frac{M L^{2}}{24}\)
4 \(\frac{M L^{2}}{3}\)
Explanation:
Moment of inertia of a uniform rod about one end \(=\frac{m L^{2}}{3} \therefore\) moment of inertia of the system \(=2 \times \frac{m}{2} \frac{(L / 2)^{2}}{3}=\frac{m L^{2}}{12}\)
269576
If \(I_{1}\) is moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre and \(I_{2}\) is its moment of inertia when it is bent into a shape of a ring then (Axis passing through its centre and perpendicular to its plane)
269577
The moment of inertia of thin rod of linear density \(\lambda\) and length \(I\) about an axis passing through one end and perpendicular to its length is
269578
Moment of inertia of a bar magnet of mass \(M\), length \(L\) and breadth \(B\) is \(I\). Then moment of inertia of another bar magnet with all these values doubled would be
1 \(8 \mathrm{I}\)
2 \(4 \mathrm{I}\)
3 \(2 I\)
4 I
Explanation:
\(I=\frac{M}{12}\left(L^{2}+b^{2}\right) \quad\)
Rotational Motion
269621
A square plate of mass \(M\) and edge \(L\) is shown in figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle \(15^{\circ}\) with the horizontal is
1 \(\frac{M L^{2}}{12}\)
2 \(\frac{11 M L^{2}}{24}\)
3 \(\frac{7 M L^{2}}{12}\)
4 \(\frac{10 M L^{2}}{24}\)
Explanation:
From diagram, we get \(x=A O \sin 60^{\circ}\)
\(=\frac{L}{\sqrt{2}} \times \frac{\sqrt{3}}{2} ; I_{z}=\frac{M L^{2}}{6} ; I_{x}=I_{y}=\frac{M L^{2}}{12}\)
\(I_{A B}=\frac{M L^{2}}{12}+M x^{2}\)
Rotational Motion
269622
A thin rod of length \(L\) and mass \(M\) is bent at the middle point \(O\) at an angle of \(60^{\circ}\). The moment of inertia of the rod about an axis passing through \(O\) and perpendicular to the plane of the rod will be
1 \(\frac{M L^{2}}{6}\)
2 \(\frac{M L^{2}}{12}\)
3 \(\frac{M L^{2}}{24}\)
4 \(\frac{M L^{2}}{3}\)
Explanation:
Moment of inertia of a uniform rod about one end \(=\frac{m L^{2}}{3} \therefore\) moment of inertia of the system \(=2 \times \frac{m}{2} \frac{(L / 2)^{2}}{3}=\frac{m L^{2}}{12}\)
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Rotational Motion
269576
If \(I_{1}\) is moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre and \(I_{2}\) is its moment of inertia when it is bent into a shape of a ring then (Axis passing through its centre and perpendicular to its plane)
269577
The moment of inertia of thin rod of linear density \(\lambda\) and length \(I\) about an axis passing through one end and perpendicular to its length is
269578
Moment of inertia of a bar magnet of mass \(M\), length \(L\) and breadth \(B\) is \(I\). Then moment of inertia of another bar magnet with all these values doubled would be
1 \(8 \mathrm{I}\)
2 \(4 \mathrm{I}\)
3 \(2 I\)
4 I
Explanation:
\(I=\frac{M}{12}\left(L^{2}+b^{2}\right) \quad\)
Rotational Motion
269621
A square plate of mass \(M\) and edge \(L\) is shown in figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle \(15^{\circ}\) with the horizontal is
1 \(\frac{M L^{2}}{12}\)
2 \(\frac{11 M L^{2}}{24}\)
3 \(\frac{7 M L^{2}}{12}\)
4 \(\frac{10 M L^{2}}{24}\)
Explanation:
From diagram, we get \(x=A O \sin 60^{\circ}\)
\(=\frac{L}{\sqrt{2}} \times \frac{\sqrt{3}}{2} ; I_{z}=\frac{M L^{2}}{6} ; I_{x}=I_{y}=\frac{M L^{2}}{12}\)
\(I_{A B}=\frac{M L^{2}}{12}+M x^{2}\)
Rotational Motion
269622
A thin rod of length \(L\) and mass \(M\) is bent at the middle point \(O\) at an angle of \(60^{\circ}\). The moment of inertia of the rod about an axis passing through \(O\) and perpendicular to the plane of the rod will be
1 \(\frac{M L^{2}}{6}\)
2 \(\frac{M L^{2}}{12}\)
3 \(\frac{M L^{2}}{24}\)
4 \(\frac{M L^{2}}{3}\)
Explanation:
Moment of inertia of a uniform rod about one end \(=\frac{m L^{2}}{3} \therefore\) moment of inertia of the system \(=2 \times \frac{m}{2} \frac{(L / 2)^{2}}{3}=\frac{m L^{2}}{12}\)
269576
If \(I_{1}\) is moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre and \(I_{2}\) is its moment of inertia when it is bent into a shape of a ring then (Axis passing through its centre and perpendicular to its plane)
269577
The moment of inertia of thin rod of linear density \(\lambda\) and length \(I\) about an axis passing through one end and perpendicular to its length is
269578
Moment of inertia of a bar magnet of mass \(M\), length \(L\) and breadth \(B\) is \(I\). Then moment of inertia of another bar magnet with all these values doubled would be
1 \(8 \mathrm{I}\)
2 \(4 \mathrm{I}\)
3 \(2 I\)
4 I
Explanation:
\(I=\frac{M}{12}\left(L^{2}+b^{2}\right) \quad\)
Rotational Motion
269621
A square plate of mass \(M\) and edge \(L\) is shown in figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle \(15^{\circ}\) with the horizontal is
1 \(\frac{M L^{2}}{12}\)
2 \(\frac{11 M L^{2}}{24}\)
3 \(\frac{7 M L^{2}}{12}\)
4 \(\frac{10 M L^{2}}{24}\)
Explanation:
From diagram, we get \(x=A O \sin 60^{\circ}\)
\(=\frac{L}{\sqrt{2}} \times \frac{\sqrt{3}}{2} ; I_{z}=\frac{M L^{2}}{6} ; I_{x}=I_{y}=\frac{M L^{2}}{12}\)
\(I_{A B}=\frac{M L^{2}}{12}+M x^{2}\)
Rotational Motion
269622
A thin rod of length \(L\) and mass \(M\) is bent at the middle point \(O\) at an angle of \(60^{\circ}\). The moment of inertia of the rod about an axis passing through \(O\) and perpendicular to the plane of the rod will be
1 \(\frac{M L^{2}}{6}\)
2 \(\frac{M L^{2}}{12}\)
3 \(\frac{M L^{2}}{24}\)
4 \(\frac{M L^{2}}{3}\)
Explanation:
Moment of inertia of a uniform rod about one end \(=\frac{m L^{2}}{3} \therefore\) moment of inertia of the system \(=2 \times \frac{m}{2} \frac{(L / 2)^{2}}{3}=\frac{m L^{2}}{12}\)
269576
If \(I_{1}\) is moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre and \(I_{2}\) is its moment of inertia when it is bent into a shape of a ring then (Axis passing through its centre and perpendicular to its plane)
269577
The moment of inertia of thin rod of linear density \(\lambda\) and length \(I\) about an axis passing through one end and perpendicular to its length is
269578
Moment of inertia of a bar magnet of mass \(M\), length \(L\) and breadth \(B\) is \(I\). Then moment of inertia of another bar magnet with all these values doubled would be
1 \(8 \mathrm{I}\)
2 \(4 \mathrm{I}\)
3 \(2 I\)
4 I
Explanation:
\(I=\frac{M}{12}\left(L^{2}+b^{2}\right) \quad\)
Rotational Motion
269621
A square plate of mass \(M\) and edge \(L\) is shown in figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle \(15^{\circ}\) with the horizontal is
1 \(\frac{M L^{2}}{12}\)
2 \(\frac{11 M L^{2}}{24}\)
3 \(\frac{7 M L^{2}}{12}\)
4 \(\frac{10 M L^{2}}{24}\)
Explanation:
From diagram, we get \(x=A O \sin 60^{\circ}\)
\(=\frac{L}{\sqrt{2}} \times \frac{\sqrt{3}}{2} ; I_{z}=\frac{M L^{2}}{6} ; I_{x}=I_{y}=\frac{M L^{2}}{12}\)
\(I_{A B}=\frac{M L^{2}}{12}+M x^{2}\)
Rotational Motion
269622
A thin rod of length \(L\) and mass \(M\) is bent at the middle point \(O\) at an angle of \(60^{\circ}\). The moment of inertia of the rod about an axis passing through \(O\) and perpendicular to the plane of the rod will be
1 \(\frac{M L^{2}}{6}\)
2 \(\frac{M L^{2}}{12}\)
3 \(\frac{M L^{2}}{24}\)
4 \(\frac{M L^{2}}{3}\)
Explanation:
Moment of inertia of a uniform rod about one end \(=\frac{m L^{2}}{3} \therefore\) moment of inertia of the system \(=2 \times \frac{m}{2} \frac{(L / 2)^{2}}{3}=\frac{m L^{2}}{12}\)
