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For which of the following does the centre of mass lie outside the body?

1. A pencil 2. A shotput 3. A dice 4. A bangle

Subtopic: Center of Mass |

86%

From NCERT

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Which of the following points is the likely position of the center of mass of the system shown in the figure?

1. \(A\)

2. \(B\)

3. \(C\)

4. \(D\)

Subtopic: Center of Mass |

74%

From NCERT

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A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to the +ve y-axis and intersecting z-axis at z a in the figure. The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is

1. mvae^{x}

2. 2mvae^{x}

3. ymvae^{x}

4. 2ymvae^{x}

Subtopic: Angular Momentum |

74%

From NCERT

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When a disc rotates with uniform angular velocity, which of the following is not true?

1. | the sense of rotation remains the same. |

2. | the orientation of the axis of rotation remains the same. |

3. | the speed of rotation is non-zero and remains the same. |

4. | the angular acceleration is non-zero and remains the same. |

Subtopic: Rotational Motion: Kinematics |

68%

From NCERT

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A uniform square plate has a small piece \(Q\) of an irregular shape removed and glued to the center of the plate leaving a hole behind in the figure. The moment of inertia about the \(\mathrm{z}\)-axis is then,

1. increased

2. decreased

3. the same

4. changed in manner

Subtopic: Moment of Inertia |

65%

From NCERT

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A uniform square plate has a small piece Q of an irregular shape removed and glued to the center of the plate leaving a hole behind in the figure. The CM of the plate is now in the following quadrant of the x-y plane.

1. I

2. II

3. III

4. IV

Subtopic: Center of Mass |

69%

From NCERT

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The density of a non-uniform rod of length 1m is given by $\mathrm{\rho}\left(\mathrm{x}\right)=\mathrm{a}(1+{\mathrm{bx}}^{2})$ where, a, and b are constants and $0\le x\le 1$. The centre of mass of the rod will be at

1. \(\frac{3(2+b)}{4(3+b)}\)

2. \(\frac{4(2+b)}{3(3+b)}\)

3. \(\frac{3(3+b)}{4(2+b)}\)

4. \(\frac{4(3+b)}{3(2+b)}\)

Subtopic: Center of Mass |

60%

From NCERT

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A merry-go-round, made of a ring-like platform of radius \(R\) and mass \(M,\) is revolving with the angular speed $\mathrm{\omega}$. A person of mass \(M\) is standing on its edge. At one instant, the person jumps off the round such that the final speed of the person is zero. What is the final angular velocity of the merry-go-round?

1. \(2\omega\)

2. \(\omega\)

3. \(\omega/2\)

4. \(0\)

$\begin{array}{l}\text{}\end{array}$

Subtopic: Angular Momentum |

61%

From NCERT

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The following are the given statements:

a. | for a general rotational motion, angular momentum \(L\) and angular velocity \(\omega\) need not be parallel. |

b. | for a rotational motion about a fixed axis, angular momentum \(L\) and angular velocity are always parallel. |

c. | for a general translational motion, momentum \(p\) and velocity \(v\) are always parallel. |

d. | for a general translational motion, acceleration \(a\) and velocity \(v\) are always parallel. |

Choose the correct option:

1. | (a), (c) |

2. | (b), (c) |

3. | (c), (d) |

4. | (a), (b), (c) |

Subtopic: Angular Momentum |

From NCERT

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The figure below shows two identical particles 1 and 2, each of mass \(m,\) moving in opposite directions with the same speed \(v\) along parallel lines. At a particular instant, \(r_1\) and \(r_2\) are their respective position vectors drawn from point A, which is in the plane of the parallel lines.

Consider the following statements.

a. | angular momentum \(l_1\) of particle 1 about A is \(l_1=mv(d_1)\) ⊙ |

b. | angular momentum \(l_1\) of particle 2 about A is \(l_1=mv(r_2)\) ⊙ |

c. | total angular momentum of the system about A is \(l=mv(r_1+r_2)\) ⊙ |

d. | total angular momentum of the system about A is \(l=mv(d_2-d_1)\) ⊗ |

Choose the correct option:

1. | (a, c) |

2. | (a, d) |

3. | (b, d) |

4. | (b, c) |

Subtopic: Angular Momentum |

70%

From NCERT

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