03. Moment of Inertia, Radius of Gyration
Rotational Motion

150130 The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is \(\frac{\mathrm{Ma}^{2}}{6}\) where \(M\) is the mass and ' \(a\) ' is the side of square plate. Moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corner is

1 \(\frac{2 \mathrm{Ma}^{2}}{3}\)
2 \(\frac{\mathrm{Ma}^{2}}{3}\)
3 \(\frac{3}{\mathrm{Ma}^{2}}\)
4 \(\frac{3 \mathrm{Ma}^{2}}{2}\)
Rotational Motion

150131 Two rings of same mass ' \(M\) ' and radius ' \(R\) ' are so placed that their centre is common and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to any one ring is

1 \(\frac{3 \mathrm{MR}^{2}}{2}\)
2 \(\mathrm{MR}^{2}\)
3 \(\frac{2 \mathrm{MR}^{2}}{3}\)
4 \(\frac{\mathrm{MR}^{2}}{2}\)
[МНТ-CET 2020]
Rotational Motion

150132 A thin uniform rod has mass ' \(M\) ' and length ' \(L\) '. The moment of inertia about an axis perpendicular to it and passing through the point at a distance \(\frac{L}{3}\) from one of its ends, will be

1 \(\frac{\mathrm{ML}^{2}}{3}\)
2 \(\frac{\mathrm{ML}^{2}}{9}\)
3 \(\frac{\mathrm{ML}^{2}}{12}\)
4 \(\frac{7}{8} \mathrm{ML}^{2}\)
Rotational Motion

150133 The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

1 \(\frac{2}{\sqrt{5}}\)
2 \(\frac{\sqrt{3}}{\sqrt{2}}\)
3 \(\frac{2}{\sqrt{3}}\)
4 \(\frac{\sqrt{2}}{1}\)
Rotational Motion

150130 The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is \(\frac{\mathrm{Ma}^{2}}{6}\) where \(M\) is the mass and ' \(a\) ' is the side of square plate. Moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corner is

1 \(\frac{2 \mathrm{Ma}^{2}}{3}\)
2 \(\frac{\mathrm{Ma}^{2}}{3}\)
3 \(\frac{3}{\mathrm{Ma}^{2}}\)
4 \(\frac{3 \mathrm{Ma}^{2}}{2}\)
Rotational Motion

150131 Two rings of same mass ' \(M\) ' and radius ' \(R\) ' are so placed that their centre is common and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to any one ring is

1 \(\frac{3 \mathrm{MR}^{2}}{2}\)
2 \(\mathrm{MR}^{2}\)
3 \(\frac{2 \mathrm{MR}^{2}}{3}\)
4 \(\frac{\mathrm{MR}^{2}}{2}\)
[МНТ-CET 2020]
Rotational Motion

150132 A thin uniform rod has mass ' \(M\) ' and length ' \(L\) '. The moment of inertia about an axis perpendicular to it and passing through the point at a distance \(\frac{L}{3}\) from one of its ends, will be

1 \(\frac{\mathrm{ML}^{2}}{3}\)
2 \(\frac{\mathrm{ML}^{2}}{9}\)
3 \(\frac{\mathrm{ML}^{2}}{12}\)
4 \(\frac{7}{8} \mathrm{ML}^{2}\)
Rotational Motion

150133 The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

1 \(\frac{2}{\sqrt{5}}\)
2 \(\frac{\sqrt{3}}{\sqrt{2}}\)
3 \(\frac{2}{\sqrt{3}}\)
4 \(\frac{\sqrt{2}}{1}\)
Rotational Motion

150130 The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is \(\frac{\mathrm{Ma}^{2}}{6}\) where \(M\) is the mass and ' \(a\) ' is the side of square plate. Moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corner is

1 \(\frac{2 \mathrm{Ma}^{2}}{3}\)
2 \(\frac{\mathrm{Ma}^{2}}{3}\)
3 \(\frac{3}{\mathrm{Ma}^{2}}\)
4 \(\frac{3 \mathrm{Ma}^{2}}{2}\)
Rotational Motion

150131 Two rings of same mass ' \(M\) ' and radius ' \(R\) ' are so placed that their centre is common and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to any one ring is

1 \(\frac{3 \mathrm{MR}^{2}}{2}\)
2 \(\mathrm{MR}^{2}\)
3 \(\frac{2 \mathrm{MR}^{2}}{3}\)
4 \(\frac{\mathrm{MR}^{2}}{2}\)
[МНТ-CET 2020]
Rotational Motion

150132 A thin uniform rod has mass ' \(M\) ' and length ' \(L\) '. The moment of inertia about an axis perpendicular to it and passing through the point at a distance \(\frac{L}{3}\) from one of its ends, will be

1 \(\frac{\mathrm{ML}^{2}}{3}\)
2 \(\frac{\mathrm{ML}^{2}}{9}\)
3 \(\frac{\mathrm{ML}^{2}}{12}\)
4 \(\frac{7}{8} \mathrm{ML}^{2}\)
Rotational Motion

150133 The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

1 \(\frac{2}{\sqrt{5}}\)
2 \(\frac{\sqrt{3}}{\sqrt{2}}\)
3 \(\frac{2}{\sqrt{3}}\)
4 \(\frac{\sqrt{2}}{1}\)
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Rotational Motion

150130 The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is \(\frac{\mathrm{Ma}^{2}}{6}\) where \(M\) is the mass and ' \(a\) ' is the side of square plate. Moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corner is

1 \(\frac{2 \mathrm{Ma}^{2}}{3}\)
2 \(\frac{\mathrm{Ma}^{2}}{3}\)
3 \(\frac{3}{\mathrm{Ma}^{2}}\)
4 \(\frac{3 \mathrm{Ma}^{2}}{2}\)
Rotational Motion

150131 Two rings of same mass ' \(M\) ' and radius ' \(R\) ' are so placed that their centre is common and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to any one ring is

1 \(\frac{3 \mathrm{MR}^{2}}{2}\)
2 \(\mathrm{MR}^{2}\)
3 \(\frac{2 \mathrm{MR}^{2}}{3}\)
4 \(\frac{\mathrm{MR}^{2}}{2}\)
[МНТ-CET 2020]
Rotational Motion

150132 A thin uniform rod has mass ' \(M\) ' and length ' \(L\) '. The moment of inertia about an axis perpendicular to it and passing through the point at a distance \(\frac{L}{3}\) from one of its ends, will be

1 \(\frac{\mathrm{ML}^{2}}{3}\)
2 \(\frac{\mathrm{ML}^{2}}{9}\)
3 \(\frac{\mathrm{ML}^{2}}{12}\)
4 \(\frac{7}{8} \mathrm{ML}^{2}\)
Rotational Motion

150133 The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

1 \(\frac{2}{\sqrt{5}}\)
2 \(\frac{\sqrt{3}}{\sqrt{2}}\)
3 \(\frac{2}{\sqrt{3}}\)
4 \(\frac{\sqrt{2}}{1}\)