# 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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A circular disk of a moment of inertia $$\mathrm{I_t}$$ is rotating in a horizontal plane, about its symmetric axis, with a constant angular speed $$\omega_i.$$ Another disk of a moment of inertia $$\mathrm{I_b}$$ is dropped coaxially onto the rotating disk. Initially, the second disk has zero angular speed. Eventually, both the disks rotate with a constant angular speed $$\omega_f.$$ The energy lost by the initially rotating disc due to friction is:
1. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{b}}^2}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

2. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{t}}^2}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

3. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{b}}-\mathrm{I}_{\mathrm{t}}}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

4. $$\frac{1}{2} \frac{\mathrm{I}_{\mathrm{b}} \mathrm{I}_{\mathrm{t}}}{\left(\mathrm{I}_{\mathrm{t}}+\mathrm{I}_{\mathrm{b}}\right)} \omega_{\mathrm{i}}^2$$

Subtopic:  Angular Momentum |
72%
From NCERT
AIPMT - 2010
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Two particles that are initially at rest, move towards each other under the action of their mutual attraction. If their speeds are $$v$$ and $$2v$$ at any instant, then the speed of the centre of mass of the system will be:
1. $$2v$$
2. $$0$$
3. $$1.5v$$
4. $$v$$

Subtopic:  Center of Mass |
78%
From NCERT
AIPMT - 2010
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A man of $$50$$ kg mass is standing in a gravity-free space at a height of $$10$$ m above the floor. He throws a stone of $$0.5$$ kg mass downwards with a speed of $$2$$ ms-1. When the stone reaches the floor, the distance of the man above the floor will be:
1. $$9.9$$ m
2. $$10.1$$ m
3. $$10$$ m
4. $$20$$ m

Subtopic:  Center of Mass |
78%
From NCERT
AIPMT - 2010
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If $$\vec F$$ is the force acting on a particle having position vector $$\vec r$$ and $$\vec \tau$$ be the torque of this force about the origin, then:

 1 $$\vec r\cdot\vec \tau\neq0\text{ and }\vec F\cdot\vec \tau=0$$ 2 $$\vec r\cdot\vec \tau>0\text{ and }\vec F\cdot\vec \tau<0$$ 3 $$\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau=0$$ 4 $$\vec r\cdot\vec \tau=0\text{ and }\vec F\cdot\vec \tau\neq0$$
Subtopic:  Torque |
82%
From NCERT
AIPMT - 2009
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A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ω. If two objects each of mass m are attached gently to the opposite ends of the diameter of the ring, the ring will then rotate with an angular velocity:

 1 $$\frac{\omega(M-2 m)}{M+2 m}$$ 2 $$\frac{\omega M}{M+2 m}$$ 3 $$\frac{\omega(M+2 m)}{M}$$ 4 $$\frac{\omega M}{M+m}$$
Subtopic:  Angular Momentum |
83%
From NCERT
AIPMT - 2009
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Two bodies of mass $$1$$ kg and $$3$$ kg have position vectors $$\hat{i}+2\hat{j}+\hat{k}$$ and $$-3\hat{i}-2\hat{j}+\hat{k}$$ respectively. The centre of mass of this system has a position vector:
1. $$-2\hat{i}+2\hat{k}$$
2. $$-2\hat{i}-\hat{j}+\hat{k}$$
3. $$2\hat{i}-\hat{j}-2\hat{k}$$
4. $$-\hat{i}+\hat{j}+\hat{k}$$

Subtopic:  Center of Mass |
88%
From NCERT
AIPMT - 2009
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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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