ROTATIONAL INERTIA OF SOLID BODIES, ROTATIONAL DYNAMICS
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Rotational Motion

269521 A metallic thin wire has uniform thickness. From this wire, two circular loops of radii\(r\), \(2 r\) are made. If moment of inertia of \(2^{\text {nd }}\) loop about its natural axis is \(\mathbf{n}\) times moment of inertia of 1st loop about its natural axis. The value of \(n\) is

1 2
2 4
3 \(2 \sqrt{2}\)
4 8
Rotational Motion

269522 The moment of inertia of a solid cylinder about an axis parallel to its length and passing through itscentre is equal to its moment of inertia about an axis perpendicular to the length of cylinder and passing through its centre. The ratio of radius of cylinder and its length is

1 \(1: \sqrt{2}\)
2 \(1: 2\)
3 \(1: \sqrt{3}\)
4 \(1: 3\)
Rotational Motion

269523 The moment of inertia of a solid cylinder about its natural axis is I. If its moment of inertia about an axis\(\perp^{r}\) to natural axis of cylinder and passing through one end of cylinder is 19I/6 then the ratio of radius of cylinder and its length is

1 \(1: 2\)
2 \(1: 3\)
3 \(1: 4\)
4 \(2: 3\)
Rotational Motion

269524 Two identical circular plates each of mass \(M\) and radius \(R\) are attached to each other with their planes \(\perp^{r}\) to eachother.The moment of inertia of system about an axis passing through their centres and the point of contact is

1 \(\frac{M R^{2}}{4}\)
2 \(\frac{5 M R^{2}}{4}\)
3 \(\frac{3}{4} M R^{2}\)
4 \(M R^{2}\)
Rotational Motion

269525 The radius of gyration of rod of length ' \(L\) ' and mass ' \(M\) ' about an axis perpendicular to its length and passing through a point at a distance \(L / 3\) from one of its ends is

1 \(\frac{\sqrt{7}}{6} L\)
2 \(\frac{L^{2}}{9}\)
3 \(\frac{L}{3}\)
4 \(\frac{\sqrt{5}}{2} L\)
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Rotational Motion

269521 A metallic thin wire has uniform thickness. From this wire, two circular loops of radii\(r\), \(2 r\) are made. If moment of inertia of \(2^{\text {nd }}\) loop about its natural axis is \(\mathbf{n}\) times moment of inertia of 1st loop about its natural axis. The value of \(n\) is

1 2
2 4
3 \(2 \sqrt{2}\)
4 8
Rotational Motion

269522 The moment of inertia of a solid cylinder about an axis parallel to its length and passing through itscentre is equal to its moment of inertia about an axis perpendicular to the length of cylinder and passing through its centre. The ratio of radius of cylinder and its length is

1 \(1: \sqrt{2}\)
2 \(1: 2\)
3 \(1: \sqrt{3}\)
4 \(1: 3\)
Rotational Motion

269523 The moment of inertia of a solid cylinder about its natural axis is I. If its moment of inertia about an axis\(\perp^{r}\) to natural axis of cylinder and passing through one end of cylinder is 19I/6 then the ratio of radius of cylinder and its length is

1 \(1: 2\)
2 \(1: 3\)
3 \(1: 4\)
4 \(2: 3\)
Rotational Motion

269524 Two identical circular plates each of mass \(M\) and radius \(R\) are attached to each other with their planes \(\perp^{r}\) to eachother.The moment of inertia of system about an axis passing through their centres and the point of contact is

1 \(\frac{M R^{2}}{4}\)
2 \(\frac{5 M R^{2}}{4}\)
3 \(\frac{3}{4} M R^{2}\)
4 \(M R^{2}\)
Rotational Motion

269525 The radius of gyration of rod of length ' \(L\) ' and mass ' \(M\) ' about an axis perpendicular to its length and passing through a point at a distance \(L / 3\) from one of its ends is

1 \(\frac{\sqrt{7}}{6} L\)
2 \(\frac{L^{2}}{9}\)
3 \(\frac{L}{3}\)
4 \(\frac{\sqrt{5}}{2} L\)
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Rotational Motion

269521 A metallic thin wire has uniform thickness. From this wire, two circular loops of radii\(r\), \(2 r\) are made. If moment of inertia of \(2^{\text {nd }}\) loop about its natural axis is \(\mathbf{n}\) times moment of inertia of 1st loop about its natural axis. The value of \(n\) is

1 2
2 4
3 \(2 \sqrt{2}\)
4 8
Rotational Motion

269522 The moment of inertia of a solid cylinder about an axis parallel to its length and passing through itscentre is equal to its moment of inertia about an axis perpendicular to the length of cylinder and passing through its centre. The ratio of radius of cylinder and its length is

1 \(1: \sqrt{2}\)
2 \(1: 2\)
3 \(1: \sqrt{3}\)
4 \(1: 3\)
Rotational Motion

269523 The moment of inertia of a solid cylinder about its natural axis is I. If its moment of inertia about an axis\(\perp^{r}\) to natural axis of cylinder and passing through one end of cylinder is 19I/6 then the ratio of radius of cylinder and its length is

1 \(1: 2\)
2 \(1: 3\)
3 \(1: 4\)
4 \(2: 3\)
Rotational Motion

269524 Two identical circular plates each of mass \(M\) and radius \(R\) are attached to each other with their planes \(\perp^{r}\) to eachother.The moment of inertia of system about an axis passing through their centres and the point of contact is

1 \(\frac{M R^{2}}{4}\)
2 \(\frac{5 M R^{2}}{4}\)
3 \(\frac{3}{4} M R^{2}\)
4 \(M R^{2}\)
Rotational Motion

269525 The radius of gyration of rod of length ' \(L\) ' and mass ' \(M\) ' about an axis perpendicular to its length and passing through a point at a distance \(L / 3\) from one of its ends is

1 \(\frac{\sqrt{7}}{6} L\)
2 \(\frac{L^{2}}{9}\)
3 \(\frac{L}{3}\)
4 \(\frac{\sqrt{5}}{2} L\)
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Rotational Motion

269521 A metallic thin wire has uniform thickness. From this wire, two circular loops of radii\(r\), \(2 r\) are made. If moment of inertia of \(2^{\text {nd }}\) loop about its natural axis is \(\mathbf{n}\) times moment of inertia of 1st loop about its natural axis. The value of \(n\) is

1 2
2 4
3 \(2 \sqrt{2}\)
4 8
Rotational Motion

269522 The moment of inertia of a solid cylinder about an axis parallel to its length and passing through itscentre is equal to its moment of inertia about an axis perpendicular to the length of cylinder and passing through its centre. The ratio of radius of cylinder and its length is

1 \(1: \sqrt{2}\)
2 \(1: 2\)
3 \(1: \sqrt{3}\)
4 \(1: 3\)
Rotational Motion

269523 The moment of inertia of a solid cylinder about its natural axis is I. If its moment of inertia about an axis\(\perp^{r}\) to natural axis of cylinder and passing through one end of cylinder is 19I/6 then the ratio of radius of cylinder and its length is

1 \(1: 2\)
2 \(1: 3\)
3 \(1: 4\)
4 \(2: 3\)
Rotational Motion

269524 Two identical circular plates each of mass \(M\) and radius \(R\) are attached to each other with their planes \(\perp^{r}\) to eachother.The moment of inertia of system about an axis passing through their centres and the point of contact is

1 \(\frac{M R^{2}}{4}\)
2 \(\frac{5 M R^{2}}{4}\)
3 \(\frac{3}{4} M R^{2}\)
4 \(M R^{2}\)
Rotational Motion

269525 The radius of gyration of rod of length ' \(L\) ' and mass ' \(M\) ' about an axis perpendicular to its length and passing through a point at a distance \(L / 3\) from one of its ends is

1 \(\frac{\sqrt{7}}{6} L\)
2 \(\frac{L^{2}}{9}\)
3 \(\frac{L}{3}\)
4 \(\frac{\sqrt{5}}{2} L\)
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Rotational Motion

269521 A metallic thin wire has uniform thickness. From this wire, two circular loops of radii\(r\), \(2 r\) are made. If moment of inertia of \(2^{\text {nd }}\) loop about its natural axis is \(\mathbf{n}\) times moment of inertia of 1st loop about its natural axis. The value of \(n\) is

1 2
2 4
3 \(2 \sqrt{2}\)
4 8
Rotational Motion

269522 The moment of inertia of a solid cylinder about an axis parallel to its length and passing through itscentre is equal to its moment of inertia about an axis perpendicular to the length of cylinder and passing through its centre. The ratio of radius of cylinder and its length is

1 \(1: \sqrt{2}\)
2 \(1: 2\)
3 \(1: \sqrt{3}\)
4 \(1: 3\)
Rotational Motion

269523 The moment of inertia of a solid cylinder about its natural axis is I. If its moment of inertia about an axis\(\perp^{r}\) to natural axis of cylinder and passing through one end of cylinder is 19I/6 then the ratio of radius of cylinder and its length is

1 \(1: 2\)
2 \(1: 3\)
3 \(1: 4\)
4 \(2: 3\)
Rotational Motion

269524 Two identical circular plates each of mass \(M\) and radius \(R\) are attached to each other with their planes \(\perp^{r}\) to eachother.The moment of inertia of system about an axis passing through their centres and the point of contact is

1 \(\frac{M R^{2}}{4}\)
2 \(\frac{5 M R^{2}}{4}\)
3 \(\frac{3}{4} M R^{2}\)
4 \(M R^{2}\)
Rotational Motion

269525 The radius of gyration of rod of length ' \(L\) ' and mass ' \(M\) ' about an axis perpendicular to its length and passing through a point at a distance \(L / 3\) from one of its ends is

1 \(\frac{\sqrt{7}}{6} L\)
2 \(\frac{L^{2}}{9}\)
3 \(\frac{L}{3}\)
4 \(\frac{\sqrt{5}}{2} L\)