Q. No.Five particles of mass \(2\) kg each are attached to the circumference of a circular disc of a radius of \(0.1\) m and negligible mass. The moment of inertia of the system about the axis passing through the centre of the disc and perpendicular to its plane will be:
1. \(1\) kg-m2
2. \(0.1\) kg-m2
3. \(2\) kg-m2
4. \(0.2\) kg-m2
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1. \(\frac{3mR^2}{2}\)
2. \(\frac{mR^2}{4}\)
3. \(\frac{mR^2}{2}\)
4. \(\frac{3mR^2}{4}\)
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1. \(\frac{Ml^2}{12}\)
2. \(\frac{Ml^2}{6}\)
3. \(\frac{Ml^2}{4}\)
4. \(\frac{Ml^2}{3}\)
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The moment of inertia of a uniform circular disc of radius '\(R\)' and mass '\(M\)' about an axis touching the disc at its diameter
and normal to the disc will be:
1. \(\frac{3}{2} M R^{2}\)
2. \(\frac{1}{2} M R^{2}\)
3. \(M R^{2}\)
4. \(\frac{2}{5} M R^{2}\)
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The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:
1. B
2. C
3. D
4. A
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The moment of inertia of a thin uniform circular disc about one of its diameter is I. Its moment of inertia about an axis perpendicular to the circular surface and passing through its center will be:
1.
2. 2 l
3.
4.
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The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the
plane of the ring will be:
1. \(2:1\)
2. :
3. \(2:3\)
4. \(1:\)
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| 1. | \(\dfrac{m_1m_2}{m_1+m_2}l^2\) | 2. | \(\dfrac{m_1+m_2}{m_1m_2}l^2\) |
| 3. | \((m_1+m_2)l^2\) | 4. | \(\sqrt{(m_1m_2)}l^2\) |
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In the three figures, each wire has a mass M, radius R and a uniform mass distribution. If they form part of a circle of radius R, then about an axis perpendicular to the plane and passing through the centre (shown by crosses), their moment of inertia is in the order:
1.
2.
3.
4.
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Three-point masses each of mass \(m,\) are placed at the vertices of an equilateral triangle of side \(a.\) The moment of inertia of the system through a mass \(m\) at \(O\) and lying in the plane of \(COD\) and perpendicular to \(OA\) is:
| 1. | \(2ma^2\) | 2. | \({2 \over 3}ma^2\) |
| 3. | \({5 \over 4}ma^2\) | 4. | \({7 \over 4}ma^2\) |
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