A solid sphere of mass \(M\) and radius \(R\) is in pure rolling with angular speed $\omega $ on a horizontal plane as shown.
The magnitude of the angular momentum of the sphere about the origin \(O\) is:

1. $\frac{7}{5}M{R}^{2}\omega $

2. $\frac{3}{2}M{R}^{2}\omega $

3. $\frac{1}{2}M{R}^{2}\omega $

4. $\frac{2}{3}M{R}^{2}\omega $

Subtopic: Angular Momentum |

81%

From NCERT

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A thin circular ring of mass *M* and radius *R* is rotating about its axis with a constant angular velocity *$\omega $*.
Four objects of mass m are held gently at the opposite ends of the ring's two perpendicular diameters. The angular velocity of the ring will be:

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

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

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

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

Subtopic: Angular Momentum |

84%

From NCERT

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A boy is standing on a disc rotating about the vertical axis passing through its centre.
He pulls his arms towards himself, reducing his moment of inertia by a factor of m. The new angular speed of the disc becomes double its initial value. If the moment of inertia of the boy is I_{0} , then the moment of inertia of the disc will be:

1. $2{\mathrm{I}}_{0}m$

2. ${\mathrm{I}}_{0}\left(1-\frac{2}{m}\right)$

3. ${\mathrm{I}}_{0}\left(1-\frac{1}{m}\right)$

4. $\left(\frac{{\mathrm{I}}_{0}}{2m}\right)$

Subtopic: Angular Momentum |

77%

From NCERT

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A rod is falling down with constant velocity \(V_0\) as shown. It makes contact with hinge A and rotates around it. The angular velocity of the rod just after the moment when it comes in contact with hinge A is:

1. | \(2 \mathrm{V}_0 / 3 \mathrm{L} \) | 2. | \(3 \mathrm{V}_0 / 2 \mathrm{L} \) |

3. | \(\mathrm{V}_0 / \mathrm{L} \) | 4. | \(2 \mathrm{V}_0 / 5 \mathrm{L}\) |

Subtopic: Angular Momentum |

72%

From NCERT

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The law of conservation of angular momentum is valid when:

1. | The net force is zero and the net torque is non-zero | 2. | The net force is non-zero and the net torque is non zero |

3. | Net force may or may not be zero and net torque is zero | 4. | Both force and torque must be zero |

Subtopic: Angular Momentum |

73%

From NCERT

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The position of a particle is given by \(\vec r = \hat i+2\hat j-\hat k\) and momentum \(\vec P = (3 \hat i + 4\hat j - 2\hat k)\). The angular momentum is perpendicular to:

1. | X-axis |

2. | Y-axis |

3. | Z-axis |

4. | Line at equal angles to all the three axes |

Subtopic: Angular Momentum |

63%

From NCERT

PMT - 2000

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A particle of mass \(m\) moves in the\(XY\) plane
with a velocity of \(v\) along the straight line \(AB.\) If the angular momentum of the particle about 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. | \(L_A<L_B\) |

Subtopic: Angular Momentum |

65%

From NCERT

AIIMS - 2007

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