ROTATIONAL INERTIAOF SOLID BODIES
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Rotational Motion

269563 Two discs one of density \(7.2 \mathrm{~g} / \mathrm{cm}^{3}\) and the other of density \(8.9 \mathrm{~g} / \mathrm{cm}^{3}\) are of same mass and thickness. Their moments of inertia are in the ratio

1 \(\frac{8.9}{7.2}\)
2 \(\frac{7.2}{8.9}\)
3 \((8.9 \times 7.2): 1\)
4 \(1:(8.9 \times 7.2)\)
Rotational Motion

269564 The mass of a circular ring is \(M\) and its radius is \(\mathbf{R}\). Its moment of inertia about an axis in the plane of ring at a perpendicular distance \(R / 2\) from centre of ring is

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

269565 Two circular rings each of mass \(M\) and radius \(R\) are attached to each other at their rims and their planes perpendicular to each other as shown in the figure. The moment of inertia of the system about a diameter of one of the rings and passing through the point of contact is

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

269566 The moment of inertia of a thin square plate of mass \(1.2 \mathrm{~kg}\) is \(0.2 \mathrm{kgm}^{2}\) when it is made to rotate about an axis perpendicular to plane of plate and passing through a corner of plate. The side length of plate is

1 \(0.2 \mathrm{~m}\)
2 \(0.4 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Rotational Motion

269567 Three point masses \(\mathbf{m}_{1}, \mathbf{m}_{2}, \mathbf{m}_{3}\) are placed at three corners of an equilateral triangle of side a. The moment of inertia of the system about an axis coinciding with the altitude of triangle passing through \(\mathrm{m}_{1}\) is

1 \(\left(m_{1}+m_{2}+m_{3}\right) a^{2}\)
2 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{6}\)
3 \(\frac{\left(m_{2}+m_{3}\right)^{2} a^{2}}{2}\)
4 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{4}\)
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Rotational Motion

269563 Two discs one of density \(7.2 \mathrm{~g} / \mathrm{cm}^{3}\) and the other of density \(8.9 \mathrm{~g} / \mathrm{cm}^{3}\) are of same mass and thickness. Their moments of inertia are in the ratio

1 \(\frac{8.9}{7.2}\)
2 \(\frac{7.2}{8.9}\)
3 \((8.9 \times 7.2): 1\)
4 \(1:(8.9 \times 7.2)\)
Rotational Motion

269564 The mass of a circular ring is \(M\) and its radius is \(\mathbf{R}\). Its moment of inertia about an axis in the plane of ring at a perpendicular distance \(R / 2\) from centre of ring is

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

269565 Two circular rings each of mass \(M\) and radius \(R\) are attached to each other at their rims and their planes perpendicular to each other as shown in the figure. The moment of inertia of the system about a diameter of one of the rings and passing through the point of contact is

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

269566 The moment of inertia of a thin square plate of mass \(1.2 \mathrm{~kg}\) is \(0.2 \mathrm{kgm}^{2}\) when it is made to rotate about an axis perpendicular to plane of plate and passing through a corner of plate. The side length of plate is

1 \(0.2 \mathrm{~m}\)
2 \(0.4 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Rotational Motion

269567 Three point masses \(\mathbf{m}_{1}, \mathbf{m}_{2}, \mathbf{m}_{3}\) are placed at three corners of an equilateral triangle of side a. The moment of inertia of the system about an axis coinciding with the altitude of triangle passing through \(\mathrm{m}_{1}\) is

1 \(\left(m_{1}+m_{2}+m_{3}\right) a^{2}\)
2 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{6}\)
3 \(\frac{\left(m_{2}+m_{3}\right)^{2} a^{2}}{2}\)
4 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{4}\)
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Rotational Motion

269563 Two discs one of density \(7.2 \mathrm{~g} / \mathrm{cm}^{3}\) and the other of density \(8.9 \mathrm{~g} / \mathrm{cm}^{3}\) are of same mass and thickness. Their moments of inertia are in the ratio

1 \(\frac{8.9}{7.2}\)
2 \(\frac{7.2}{8.9}\)
3 \((8.9 \times 7.2): 1\)
4 \(1:(8.9 \times 7.2)\)
Rotational Motion

269564 The mass of a circular ring is \(M\) and its radius is \(\mathbf{R}\). Its moment of inertia about an axis in the plane of ring at a perpendicular distance \(R / 2\) from centre of ring is

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

269565 Two circular rings each of mass \(M\) and radius \(R\) are attached to each other at their rims and their planes perpendicular to each other as shown in the figure. The moment of inertia of the system about a diameter of one of the rings and passing through the point of contact is

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

269566 The moment of inertia of a thin square plate of mass \(1.2 \mathrm{~kg}\) is \(0.2 \mathrm{kgm}^{2}\) when it is made to rotate about an axis perpendicular to plane of plate and passing through a corner of plate. The side length of plate is

1 \(0.2 \mathrm{~m}\)
2 \(0.4 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Rotational Motion

269567 Three point masses \(\mathbf{m}_{1}, \mathbf{m}_{2}, \mathbf{m}_{3}\) are placed at three corners of an equilateral triangle of side a. The moment of inertia of the system about an axis coinciding with the altitude of triangle passing through \(\mathrm{m}_{1}\) is

1 \(\left(m_{1}+m_{2}+m_{3}\right) a^{2}\)
2 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{6}\)
3 \(\frac{\left(m_{2}+m_{3}\right)^{2} a^{2}}{2}\)
4 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{4}\)
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Rotational Motion

269563 Two discs one of density \(7.2 \mathrm{~g} / \mathrm{cm}^{3}\) and the other of density \(8.9 \mathrm{~g} / \mathrm{cm}^{3}\) are of same mass and thickness. Their moments of inertia are in the ratio

1 \(\frac{8.9}{7.2}\)
2 \(\frac{7.2}{8.9}\)
3 \((8.9 \times 7.2): 1\)
4 \(1:(8.9 \times 7.2)\)
Rotational Motion

269564 The mass of a circular ring is \(M\) and its radius is \(\mathbf{R}\). Its moment of inertia about an axis in the plane of ring at a perpendicular distance \(R / 2\) from centre of ring is

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

269565 Two circular rings each of mass \(M\) and radius \(R\) are attached to each other at their rims and their planes perpendicular to each other as shown in the figure. The moment of inertia of the system about a diameter of one of the rings and passing through the point of contact is

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

269566 The moment of inertia of a thin square plate of mass \(1.2 \mathrm{~kg}\) is \(0.2 \mathrm{kgm}^{2}\) when it is made to rotate about an axis perpendicular to plane of plate and passing through a corner of plate. The side length of plate is

1 \(0.2 \mathrm{~m}\)
2 \(0.4 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Rotational Motion

269567 Three point masses \(\mathbf{m}_{1}, \mathbf{m}_{2}, \mathbf{m}_{3}\) are placed at three corners of an equilateral triangle of side a. The moment of inertia of the system about an axis coinciding with the altitude of triangle passing through \(\mathrm{m}_{1}\) is

1 \(\left(m_{1}+m_{2}+m_{3}\right) a^{2}\)
2 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{6}\)
3 \(\frac{\left(m_{2}+m_{3}\right)^{2} a^{2}}{2}\)
4 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{4}\)
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Rotational Motion

269563 Two discs one of density \(7.2 \mathrm{~g} / \mathrm{cm}^{3}\) and the other of density \(8.9 \mathrm{~g} / \mathrm{cm}^{3}\) are of same mass and thickness. Their moments of inertia are in the ratio

1 \(\frac{8.9}{7.2}\)
2 \(\frac{7.2}{8.9}\)
3 \((8.9 \times 7.2): 1\)
4 \(1:(8.9 \times 7.2)\)
Rotational Motion

269564 The mass of a circular ring is \(M\) and its radius is \(\mathbf{R}\). Its moment of inertia about an axis in the plane of ring at a perpendicular distance \(R / 2\) from centre of ring is

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

269565 Two circular rings each of mass \(M\) and radius \(R\) are attached to each other at their rims and their planes perpendicular to each other as shown in the figure. The moment of inertia of the system about a diameter of one of the rings and passing through the point of contact is

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

269566 The moment of inertia of a thin square plate of mass \(1.2 \mathrm{~kg}\) is \(0.2 \mathrm{kgm}^{2}\) when it is made to rotate about an axis perpendicular to plane of plate and passing through a corner of plate. The side length of plate is

1 \(0.2 \mathrm{~m}\)
2 \(0.4 \mathrm{~m}\)
3 \(0.5 \mathrm{~m}\)
4 \(0.8 \mathrm{~m}\)
Rotational Motion

269567 Three point masses \(\mathbf{m}_{1}, \mathbf{m}_{2}, \mathbf{m}_{3}\) are placed at three corners of an equilateral triangle of side a. The moment of inertia of the system about an axis coinciding with the altitude of triangle passing through \(\mathrm{m}_{1}\) is

1 \(\left(m_{1}+m_{2}+m_{3}\right) a^{2}\)
2 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{6}\)
3 \(\frac{\left(m_{2}+m_{3}\right)^{2} a^{2}}{2}\)
4 \(\frac{\left(m_{2}+m_{3}\right) a^{2}}{4}\)