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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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A wheel has an angular acceleration of \(3.0\) rad/s^{2} 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 |

76%

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. | \(L_A<L_B\) |

Subtopic: Angular Momentum |

69%

From NCERT

AIPMT - 2007

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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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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 |

74%

From NCERT

AIPMT - 2006

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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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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. \(\frac{1}{3}Ml^2\)

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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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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