ROTATIONAL INERTIA OF SOLID BODIES, ROTATIONAL DYNAMICS
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Rotational Motion

269517 \(I\) is moment of inertia of a thin circular plate about its natural axis. The moment of inertia of a circular ring whose mass is half of mass of plate but radius is twice the radius of plate about an axis passing through any tangent of ring in its plane is

1 \(3 I\)
2 \(4 I\)
3 \(6 I\)
4 \(1.5 \mathrm{I}\)
Rotational Motion

269518 The moment of inertia of a uniform rod of length 21 and mass \(m\) about an axis \(x y\) passing through itscentre and inclined at an enable \(\alpha\) is

1 \(\frac{m l^{2}}{3} \sin ^{2} \alpha\)
2 \(\frac{\mathrm{m} l^{2}}{12} \sin ^{2} \alpha\)
3 \(\frac{m l^{2}}{6} \cos ^{2} \alpha\)
4 \(\frac{\mathrm{ml}{ }^{2}}{2} \cos ^{2} \alpha\)
Rotational Motion

269519 The ratio of radii of two solid spheres of same material is\(1: 2\). The ratio of moments of inertia of smaller and larger spheres about axes passing through their centres is

1 \(1: 4\)
2 \(1: 8\)
3 \(1: 16\)
4 \(1: 32\)
Rotational Motion

269520 \(I\) is moment of inertia of a thin circular ring about an axis perpendicular to the plane of ring and passing through its centre. The same ring is folded into 2 turns coil. The moment of inertia of circular coil about an axis perpendicular to the plane of coil and passing through its centre is

1 \(2 I\)
2 \(4 I\)
3 \(\frac{I}{2}\)
4 \(\frac{I}{4}\)
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Rotational Motion

269517 \(I\) is moment of inertia of a thin circular plate about its natural axis. The moment of inertia of a circular ring whose mass is half of mass of plate but radius is twice the radius of plate about an axis passing through any tangent of ring in its plane is

1 \(3 I\)
2 \(4 I\)
3 \(6 I\)
4 \(1.5 \mathrm{I}\)
Rotational Motion

269518 The moment of inertia of a uniform rod of length 21 and mass \(m\) about an axis \(x y\) passing through itscentre and inclined at an enable \(\alpha\) is

1 \(\frac{m l^{2}}{3} \sin ^{2} \alpha\)
2 \(\frac{\mathrm{m} l^{2}}{12} \sin ^{2} \alpha\)
3 \(\frac{m l^{2}}{6} \cos ^{2} \alpha\)
4 \(\frac{\mathrm{ml}{ }^{2}}{2} \cos ^{2} \alpha\)
Rotational Motion

269519 The ratio of radii of two solid spheres of same material is\(1: 2\). The ratio of moments of inertia of smaller and larger spheres about axes passing through their centres is

1 \(1: 4\)
2 \(1: 8\)
3 \(1: 16\)
4 \(1: 32\)
Rotational Motion

269520 \(I\) is moment of inertia of a thin circular ring about an axis perpendicular to the plane of ring and passing through its centre. The same ring is folded into 2 turns coil. The moment of inertia of circular coil about an axis perpendicular to the plane of coil and passing through its centre is

1 \(2 I\)
2 \(4 I\)
3 \(\frac{I}{2}\)
4 \(\frac{I}{4}\)
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Rotational Motion

269517 \(I\) is moment of inertia of a thin circular plate about its natural axis. The moment of inertia of a circular ring whose mass is half of mass of plate but radius is twice the radius of plate about an axis passing through any tangent of ring in its plane is

1 \(3 I\)
2 \(4 I\)
3 \(6 I\)
4 \(1.5 \mathrm{I}\)
Rotational Motion

269518 The moment of inertia of a uniform rod of length 21 and mass \(m\) about an axis \(x y\) passing through itscentre and inclined at an enable \(\alpha\) is

1 \(\frac{m l^{2}}{3} \sin ^{2} \alpha\)
2 \(\frac{\mathrm{m} l^{2}}{12} \sin ^{2} \alpha\)
3 \(\frac{m l^{2}}{6} \cos ^{2} \alpha\)
4 \(\frac{\mathrm{ml}{ }^{2}}{2} \cos ^{2} \alpha\)
Rotational Motion

269519 The ratio of radii of two solid spheres of same material is\(1: 2\). The ratio of moments of inertia of smaller and larger spheres about axes passing through their centres is

1 \(1: 4\)
2 \(1: 8\)
3 \(1: 16\)
4 \(1: 32\)
Rotational Motion

269520 \(I\) is moment of inertia of a thin circular ring about an axis perpendicular to the plane of ring and passing through its centre. The same ring is folded into 2 turns coil. The moment of inertia of circular coil about an axis perpendicular to the plane of coil and passing through its centre is

1 \(2 I\)
2 \(4 I\)
3 \(\frac{I}{2}\)
4 \(\frac{I}{4}\)
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Rotational Motion

269517 \(I\) is moment of inertia of a thin circular plate about its natural axis. The moment of inertia of a circular ring whose mass is half of mass of plate but radius is twice the radius of plate about an axis passing through any tangent of ring in its plane is

1 \(3 I\)
2 \(4 I\)
3 \(6 I\)
4 \(1.5 \mathrm{I}\)
Rotational Motion

269518 The moment of inertia of a uniform rod of length 21 and mass \(m\) about an axis \(x y\) passing through itscentre and inclined at an enable \(\alpha\) is

1 \(\frac{m l^{2}}{3} \sin ^{2} \alpha\)
2 \(\frac{\mathrm{m} l^{2}}{12} \sin ^{2} \alpha\)
3 \(\frac{m l^{2}}{6} \cos ^{2} \alpha\)
4 \(\frac{\mathrm{ml}{ }^{2}}{2} \cos ^{2} \alpha\)
Rotational Motion

269519 The ratio of radii of two solid spheres of same material is\(1: 2\). The ratio of moments of inertia of smaller and larger spheres about axes passing through their centres is

1 \(1: 4\)
2 \(1: 8\)
3 \(1: 16\)
4 \(1: 32\)
Rotational Motion

269520 \(I\) is moment of inertia of a thin circular ring about an axis perpendicular to the plane of ring and passing through its centre. The same ring is folded into 2 turns coil. The moment of inertia of circular coil about an axis perpendicular to the plane of coil and passing through its centre is

1 \(2 I\)
2 \(4 I\)
3 \(\frac{I}{2}\)
4 \(\frac{I}{4}\)
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