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A circular ring of mass M and radius R is rotating about its axis with constant angular velocity ω. Two particles, each of mass m are attached gently to the opposite ends of the diameter of the ring. The angular velocity of the ring will now become:

1. \(\frac{m \omega}{M + 2 m}\)

2. \(\frac{m \omega}{M - 2 m}\)

3. \(\frac{M \omega}{M + 2 m}\)

4. \(\frac{M + 2 m}{M \omega}\)

Subtopic: Angular Momentum |

82%

From NCERT

AIPMT - 1998

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In the figure given below, O is the centre of an equilateral triangle ABC and $\overrightarrow{{\mathrm{F}}_{1}},$ $$ $\overrightarrow{{\mathrm{F}}_{2}},$ $$ $\overrightarrow{{\mathrm{F}}_{3}}$ are three forces acting along the sides AB, BC and AC. What should be the magnitude of $\overrightarrow{{F}_{3}}$ $$ so that total torque about O is zero?

1. $|$ ${\overrightarrow{F}}_{3}|$ $=$ $\left|\overrightarrow{{F}_{1}}\right|$ $+$ $|\overrightarrow{{F}_{2}|}$

2. $|$ $\overrightarrow{{F}_{3}}|$ $=$ $\left|\overrightarrow{{F}_{1}}\right|$ $-$ $|\overrightarrow{{F}_{2}|}$

3. $|$ $\overrightarrow{{F}_{3}}|$ $=$ $\overrightarrow{{F}_{1}}$ $+$ $2\overrightarrow{{F}_{2}}$

4. Not possible

Subtopic: Torque |

81%

From NCERT

AIPMT - 1998

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For a body, with angular velocity \( \vec{\omega }=\hat{i}-2\hat{j}+3\hat{k}\) and radius vector \( \vec{r }=\hat{i}+\hat{j}++\hat{k},\) its velocity will be:

1. \(-5\hat{i}+2\hat{j}+3\hat{k}\)

2. \(-5\hat{i}+2\hat{j}-3\hat{k}\)

3. \(-5\hat{i}-2\hat{j}+3\hat{k}\)

4. \(-5\hat{i}-2\hat{j}-3\hat{k}\)

Subtopic: Rotational Motion: Kinematics |

68%

From NCERT

AIPMT - 1999

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When a stick is released (as shown in the figure below), its free end velocity when it strikes the ground is:

1. 4.2 m/s

2. 1.4 m/s

3. 2.8 m/s

4. $\sqrt{6}$ m/s

Subtopic: Center of Mass |

From NCERT

AIPMT - 1999

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For the diagram given below, a triangular lamina is shown. The correct relation between I_{1}, I_{2} & I_{3} is (I – moment of inertia)

1. I_{1} > I_{2 }

2. I_{2} > I_{1}

3. I_{3} > I_{1 }

4. I_{3} > I_{2}

Subtopic: Moment of Inertia |

68%

From NCERT

AIPMT - 2000

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A circular disc is to be made by using iron and aluminium so that it acquires a maximum moment of inertia about its geometrical axis. It is possible with:

1. | Aluminium in the interior and iron surrounding it |

2. | Iron at the interior and aluminium surrounding it |

3. | Using iron and aluminium layers in alternate order |

4. | A sheet of iron is used at both the external surface and aluminium sheet as the internal layer |

Subtopic: Moment of Inertia |

71%

From NCERT

AIPMT - 2002

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A disc is rotating with angular speed \(\omega.\) If a child sits on it, what is conserved here?

1. Linear momentum

2. Angular momentum

3. Kinetic energy

4. Potential energy

Subtopic: Angular Momentum |

91%

From NCERT

AIPMT - 2002

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If a rod of length 3 m with its mass acting per unit length, is directly proportional to distance x from one of its ends, then its centre of gravity from that end will be at:

1. | 1.5 m | 2. | 2 m |

3. | 2.5 m | 4. | 3.0 m |

Subtopic: Center of Mass |

58%

From NCERT

AIPMT - 2002

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A thin circular ring \(\mathrm{M}\) and radius \(\mathrm{r}\) is rotating about its axis with a constant angular velocity ω. Four objects, each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be:

1. $\frac{\mathrm{M\omega}}{4\mathrm{m}}$

2. $\frac{\mathrm{M\omega}}{\mathrm{M}+4\mathrm{m}}$

3. $\frac{(\mathrm{M}+4\mathrm{m})\mathrm{\omega}}{\mathrm{M}}$

4. $\frac{(\mathrm{M}+4\mathrm{m})\mathrm{\omega}}{\mathrm{M}+4\mathrm{m}}$

Subtopic: Angular Momentum |

93%

From NCERT

AIPMT - 2003

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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. $\sqrt{5}$ : $\sqrt{6}$

3. \(2:3\)

4. \(1:\) $\sqrt{2}$

Subtopic: Moment of Inertia |

74%

From NCERT

AIPMT - 2004

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