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Given the following statements:

a: |
The centre of gravity (C.G.) of a body is the point at which the weight of the body acts. |

b: |
If the earth is assumed to have an infinitely large radius, the centre of mass coincides with the centre of gravity. |

c. |
To evaluate the gravitational field intensity due to any body at an external point, the entire mass of the body can be considered to be concentrated at its C.G. |

d. |
The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C.G. of the body to the axis. |

Which one of the following pairs of statements is correct?

1. **(a)** and **(b)**

2. **(b) **and **(c)**

3. **(c) **and **(d)**

4. **(d) **and **(a)**

Subtopic: Center of Mass |

From NCERT

AIPMT - 2010

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From a circular disc of radius \(R\) and mass \(9M,\) a small disc of mass \(M\) and radius \(R/3\) is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is:

1. \(MR^{2}\)

2. \(4MR^{2}\)

3. \(\frac{4}{9}MR^{2}\)

4. \(\frac{40}{9}MR^{2}\)

Subtopic: Moment of Inertia |

71%

From NCERT

AIPMT - 2010

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A thin circular ring of mass \(M\) and radius \(r\) is rotating about its axis with constant angular velocity ω. Two objects each of mass \(m\) are attached gently to the opposite ends of the diameter of the ring. The ring now rotates with angular velocity given by:

1. $\frac{2M\omega}{M+2m}$

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

3. $\frac{M\omega}{M+2m}$

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

Subtopic: Angular Momentum |

84%

From NCERT

AIPMT - 2010

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Three masses are placed on the \(x\)-axis: \(300~\text{g}\) at origin, \(500~\text{g}\) at \(x= 40~\text{cm}\) and \(400~\text{g}\) at \(x= 70~\text{cm}\). The distance of the centre of mass from the origin is:

1. \(45~\text{cm}\)

2. \(50~\text{cm}\)

3. \(30~\text{cm}\)

4. \(40~\text{cm}\)

Subtopic: Center of Mass |

81%

From NCERT

AIPMT - 2012

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A circular platform is mounted on a frictionless vertical axle. Its radius \(R = 2~\text{m}\) and its moment of inertia about the axle is \(200~\text{kg m}^2\). It is initially at rest. A \(50~\text{kg}\) man stands on the edge of the platform and begins to walk along the edge at the speed of \(1~\text{ms}^{-1}\) relative to the ground. The time taken by man to complete one revolution is:

1. \(\frac{3\pi}{2}\text{s}\)

2. \(2\pi~\text{s}\)

3. \(\frac{\pi}{2}\text{s}\)

4. \(\pi~\text{s}\)

Subtopic: Angular Momentum |

64%

From NCERT

AIPMT - 2012

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The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through:

1. \(C\)

2. \(D\)

3. \(A\)

4. \(B\)

Subtopic: Moment of Inertia |

79%

From NCERT

AIPMT - 2012

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The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centers and perpendicular to their planes are:

1. \(1 : \sqrt 2\)

2. \(3:2\)

3. \(2:1\)

4. \( \sqrt 2 : 1 \)

1. \(1 : \sqrt 2\)

2. \(3:2\)

3. \(2:1\)

4. \( \sqrt 2 : 1 \)

Subtopic: Moment of Inertia |

77%

From NCERT

NEET - 2013

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Two discs are rotating about their respective axes, which are normal to the discs and pass through their centres. Disc \(D_1\) has a \(2\) kg mass and \(0.2\) m radius and an initial angular velocity of \(50\) rad s^{–1}. Disc \(D_2\) has a \(4\) kg mass, \(0.1\) m radius and an initial angular velocity of \(200\) rad s^{–1}. When the two discs are brought into contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s^{–1}) of the combined system is:

1. \(60\)

2. \(100\)

3. \(120\)

4. \(40\)

1. \(60\)

2. \(100\)

3. \(120\)

4. \(40\)

Subtopic: Angular Momentum |

76%

From NCERT

NEET - 2013

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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 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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