Point masses $$m_1$$ and $$m_2$$, are placed at the opposite ends of a rigid rod of length $$L$$ and negligible mass. The rod is set into rotation about an axis perpendicular to it. The position of point $$P$$ on this rod through which the axis should pass so that the ork required to set the rod rotating with angular velocity ${\mathrm{\omega }}_{0}$ is minimum is given by:

 1 $$x = \frac{m_1L}{m_1+m_2}$$ 2 $$x= \frac{m_1}{m_2}L$$ 3 $$x= \frac{m_2}{m_1}L$$ 4 $$x = \frac{m_2L}{m_1+m_2}$$

Subtopic:  Moment of Inertia |
72%
From NCERT
NEET - 2015
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Three identical spherical shells, each of mass $$m$$ and radius $$r$$ are placed as shown in the figure. Consider an axis $$XX'$$, which is touching two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about the $$XX'$$ axis is:

 1 $$\frac{11}{5}mr^2$$ 2 $$3mr^2$$ 3 $$\frac{16}{5}mr^2$$ 4 $$4mr^2$$

Subtopic:  Moment of Inertia |
61%
From NCERT
NEET - 2015
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The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centers and perpendicular to their planes are:
1. $$1 : \sqrt 2$$
2. $$3:2$$
3. $$2:1$$
4. $$\sqrt 2 : 1$$
Subtopic:  Moment of Inertia |
77%
From NCERT
NEET - 2013
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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. $$C$$
2. $$D$$
3. $$A$$
4. $$B$$

Subtopic:  Moment of Inertia |
79%
From NCERT
AIPMT - 2012
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The moment of inertia of a thin uniform rod of mass $$M$$ and length $$L$$ about an axis passing through its mid-point and perpendicular to its length is $$I_0$$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is:
1. $$I_0+\frac{ML^2}{4}$$
2. $$I_0+2ML^2$$
3. $$I_0+ML^2$$
4. $$I_0+\frac{ML^2}{2}$$

Subtopic:  Moment of Inertia |
80%
From NCERT
AIPMT - 2011
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From a circular disc of radius $$R$$ and mass $$9M,$$ a small disc of mass $$M$$ and radius $$R/3$$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is:
1. $$MR^{2}$$
2. $$4MR^{2}$$
3. $$\frac{4}{9}MR^{2}$$
4. $$\frac{40}{9}MR^{2}$$

Subtopic:  Moment of Inertia |
71%
From NCERT
AIPMT - 2010
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Four identical thin rods, each of mass $$M$$ and length $$l$$, form a square frame. The moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is:
1. $$\frac{4}{3}Ml^2$$
2. $$\frac{2}{3}Ml^2$$
3. $$\frac{13}{3}Ml^2$$
4. $$\frac{1}{3}Ml^2$$

Subtopic:  Moment of Inertia |
75%
From NCERT
AIPMT - 2009
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The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:

 1 $$\sqrt{3}:\sqrt{2}$$ 2 $$1:\sqrt{2}$$ 3 $$\sqrt{2}:1$$ 4 $$\sqrt{2}:\sqrt{3}$$
Subtopic:  Moment of Inertia |
82%
From NCERT
AIPMT - 2008
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A thin rod of length $$L$$ and mass $$M$$ is bent at its midpoint into two halves so that the angle between them is $$90^{\circ}$$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:
1.  $$\frac{ML^2}{24}$$
2.  $$\frac{ML^2}{12}$$
3.  $$\frac{ML^2}{6}$$
4.  $$\frac{\sqrt{2}ML^2}{24}$$

Subtopic:  Moment of Inertia |
70%
From NCERT
AIPMT - 2008
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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 is:
1. $M{R}^{2}$

2. $\frac{2}{5}M{R}^{2}$

3. $\frac{3}{2}M{R}^{2}$

4. $\frac{1}{2}M{R}^{2}$

Subtopic:  Moment of Inertia |
68%
From NCERT
AIPMT - 2006
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