# 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 |
81%
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 |
69%
From NCERT
AIPMT - 2008
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A wheel has an angular acceleration of $$3.0$$ rad/s2 and an initial angular speed of $$2.0$$ rad/s. In a time of $$2$$ s, it has rotated through an angle (in radians) of:

 1 $$6$$ 2 $$10$$ 3 $$12$$ 4 $$4$$

Subtopic:  Rotational Motion: Kinematics |
83%
From NCERT
AIPMT - 2007
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A uniform rod AB of length $$l$$ and mass $$m$$ is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is $$\frac{ml^2}{3}$$ the initial angular acceleration of the rod will be:

1. $$\frac{2g}{3l}$$
2. $$\frac{mgl}{2}$$
3. $$\frac{3}{2}gl$$
4. $$\frac{3g}{2l}$$

Subtopic:  Rotational Motion: Dynamics |
75%
From NCERT
AIPMT - 2007
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A particle of mass $$m$$ moves in the XY plane with a velocity $$v$$ along the straight line AB. If the angular momentum of the particle with respect to the origin $$O$$ is $$L_A$$ when it is at $$A$$ and $$L_B$$ when it is at $$B,$$ then:

 1 $$L_A>L_B$$ 2 $$L_A=L_B$$ 3 the relationship between $$L_A$$ and $$L_B$$ depends upon the slope of the line $$AB.$$ 4 $$L_A Subtopic: Angular Momentum | 69% From NCERT AIPMT - 2007 To view explanation, please take trial in the course. NEET 2023 - Target Batch - Aryan Raj Singh Hints Links To view explanation, please take trial in the course. NEET 2023 - Target Batch - Aryan Raj Singh 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 |
67%
From NCERT
AIPMT - 2006
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A uniform rod of length $$l$$ and mass $$M$$ is free to rotate in a vertical plane about $$A$$. The rod, initially in the horizontal position, is released. The initial angular acceleration of the rod is: (Moment of inertia of the rod about $$A$$ is $$\frac{Ml^2}{3}$$)
1. $$\frac{3g}{2l}$$
2. $$\frac{2l}{3g}$$
3. $$\frac{3g}{2l^2}$$
4. $$\frac{Mg}{2}$$

Subtopic:  Torque |
73%
From NCERT
AIPMT - 2006
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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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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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