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If \(A\) is the areal velocity of a planet of mass \(M,\) then its angular momentum is:

1. | \(\frac{M}{A}\) | 2. | \(2MA\) |

3. | \(A^2M\) | 4. | \(AM^2\) |

Subtopic: Kepler's Laws |

74%

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The figure shows the elliptical orbit of a planet \(m\) about the sun \(\mathrm{S}.\) The shaded area \(\mathrm{SCD}\) is twice the shaded area \(\mathrm{SAB}.\) If \(t_1\) is the time for the planet to move from \(\mathrm{C}\) to \(\mathrm{D}\) and \(t_2\) is the time to move from \(\mathrm{A}\) to \(\mathrm{B},\) then:

1. | \(t_1>t_2\) | 2. | \(t_1=4t_2\) |

3. | \(t_1=2t_2\) | 4. | \(t_1=t_2\) |

Subtopic: Kepler's Laws |

71%

From NCERT

AIPMT - 2009

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Let the speed of the planet at the perihelion \(P\) in figure shown below be \(v_{_P}\) and the Sun-planet distance \(\mathrm{SP}\) be \(r_{_P}.\) Relation between \((r_{_P},~v_{_P})\) to the corresponding quantities at the aphelion \((r_{_A},~v_{_A})\) is:

1. | \(v_{_P} r_{_P} =v_{_A} r_{_A}\) | 2. | \(v_{_A} r_{_P} =v_{_P} r_{_A}\) |

3. | \(v_{_A} v_{_P} = r_{_A}r_{_P}\) | 4. | none of these |

Subtopic: Kepler's Laws |

78%

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Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?

1. | speed |

2. | angular speed |

3. | kinetic energy |

4. | angular momentum |

Subtopic: Kepler's Laws |

85%

From NCERT

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Two planets are in a circular orbit of radius \(R\) and \(4R\) about a star. At a specific time, the two planets and the star are in a straight line. If the period of the closest planet is \(T,\) then the star and planets will again be in a straight line after a minimum time:

2. \((4)^{\frac13}T\)

3. \(2T\)

4. \(8T\)

Subtopic: Kepler's Laws |

64%

From NCERT

NEET - 2022

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The planet Mars has two moons, Phobos and Delmos. Phobos has a period of \(7\) hours, \(39\) minutes and an orbital radius of \(9 . 4 \times 10^{3}\) km. The mass of mars is:

1. | \(6 . 48 \times 10^{23} \text{ kg}\) | 2. | \(6 . 48 \times 10^{25} \text{ kg}\) |

3. | \(6 . 48 \times 10^{20} \text{ kg}\) | 4. | \(6 . 48 \times 10^{21} \text{ kg}\) |

Subtopic: Satellite |

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The force of gravitation between a particle \(A,\) and another particle \(B\) when separated by a distance \(r\) is \(F_{AB};\) while the force between a particle \(C\) and \(A\) separated by the same distance is \(4F_{AB}.\) The ratio of the masses of \(B\) and \(C\) is:

1. \(4\)

2. \(2\)

3. \(\frac12\)

4. \(\frac14\)

1. \(4\)

2. \(2\)

3. \(\frac12\)

4. \(\frac14\)

Subtopic: Newton's Law of Gravitation |

81%

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Three equal masses of \(m\) kg each are fixed at the vertices of an equilateral triangle \(ABC.\) What is the force acting on a mass \(2m\) placed at the centroid \(G\) of the triangle?

(Take \(AG=BG=CG=1\) m.)

1. \(Gm^2(\hat{i}+\hat{j})\)

2. \(Gm^2(\hat{i}-\hat{j})\)

3. zero

4. \(2Gm^2(\hat{i}+\hat{j})\)

Subtopic: Newton's Law of Gravitation |

83%

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Two spheres of masses \(m\) and \(M\) are situated in air and the gravitational force between them is \(F.\) If the space around the masses is filled with a liquid of specific density \(3,\) the gravitational force will become:

1. \(3F\)

2. \(F\)

3. \(F/3\)

4. \(F/9\)

Subtopic: Newton's Law of Gravitation |

82%

From NCERT

AIPMT - 2003

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If a particle is projected vertically upward with a speed \(u,\) and rises to a maximum altitude \(h\) above the earth's surface then (\(g=\) acceleration due to gravity at surface)

1. | \(h>\frac{u^2}{2g}\) |

2. | \(h=\frac{u^2}{2g}\) |

3. | \(h<\frac{u^2}{2g}\) |

4. | Any of the above maybe true, depending on the earth's radius |

Subtopic: Acceleration due to Gravity |

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