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The distance of a planet from the sun is \(5\) times the distance between the earth and the sun. The time period of the planet is:

1. | \(5^{3/2}\) years | 2. | \(5^{2/3}\) years |

3. | \(5^{1/3}\) years | 4. | \(5^{1/2}\) years |

Subtopic: Kepler's Laws |

80%

From NCERT

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A planet moves around the sun. At a point P, it is closest to the sun at a distance \(d_1\) and has speed \(v_1.\) At another point Q, when it is farthest from the sun at distance \(d_2,\) its speed will be:

1. | \(d_2v_1 \over d_1\) | 2. | \(d_1v_1 \over d_2\) |

3. | \(d_1^2v_1 \over d_2\) | 4. | \(d_2^2v_1 \over d_1\) |

Subtopic: Kepler's Laws |

81%

From NCERT

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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%

From NCERT

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Kepler's third law states that the square of the period of revolution (\(T\)) of a planet around the sun, is proportional to the third power of average distance \(r\) between the sun and planet i.e. \(T^2 = Kr^3\), here \(K\) is constant. If the masses of the sun and planet are \(M\) and \(m\) respectively, then as per Newton's law of gravitation, the force of attraction between them is \(F = \frac{GMm}{r^2},\) here \(G\) is the gravitational constant. The relation between \(G\) and \(K\) is described as:

1. \(GK = 4\pi^2\)

2. \(GMK = 4\pi^2\)

3. \(K =G\)

4. \(K = \frac{1}{G}\)

Subtopic: Kepler's Laws |

79%

From NCERT

NEET - 2015

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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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If R is the radius of the orbit of a planet and T is the time period of the planet, then which of the following graphs correctly shows the motion of a planet revolving around the sun?

1. | 2. | ||

3. | 4. |

Subtopic: Kepler's Laws |

78%

From NCERT

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If two planets are at mean distances ${d}_{1}$ and ${d}_{2}$ from the sun and their frequencies are *n*_{1} and *n*_{2} respectively, then:

1. ${{n}_{1}}^{2}{{d}_{1}}^{2}={n}_{2}{{d}_{2}}^{2}$

2. ${{n}_{2}}^{2}{{d}_{2}}^{3}={{n}_{1}}^{2}{{d}_{1}}^{3}$

3. ${n}_{1}{{d}_{1}}^{2}={n}_{2}{{d}_{2}}^{2}$

4. ${{n}_{1}}^{2}{d}_{1}={{n}_{2}}^{2}{d}_{2}$

Subtopic: Kepler's Laws |

67%

From NCERT

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The figure shows a planet in an elliptical orbit around the sun (S). The ratio of the momentum of the planet at point A to that at point B is:

1. | $\frac{{\mathrm{r}}_{1}}{{\mathrm{r}}_{2}}$ | 2. | $\frac{{{\mathrm{r}}_{1}}^{2}}{{{\mathrm{r}}_{2}}^{2}}$ |

3. | $\frac{{\mathrm{r}}_{2}}{{\mathrm{r}}_{1}}$ | 4. | $\frac{{{\mathrm{r}}_{2}}^{2}}{{{\mathrm{r}}_{1}}^{2}}$ |

Subtopic: Kepler's Laws |

60%

From NCERT

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Two satellites S_{1} and S_{2} are revolving around a planet in coplanar and concentric circular orbits of radii R_{1 }and R_{2} in the same direction respectively. Their respective periods of revolution are 1 hr and 8 hr. The radius of the orbit of satellite S_{1} is equal to 10^{4} km. Find the relative speed when they are closest to each other.

1. $2\mathrm{\pi}\times {10}^{4}$ $\mathrm{kmph}$

2. $\mathrm{\pi}\times {10}^{4}$ $\mathrm{kmph}$

3. $\frac{\mathrm{\pi}}{2}\times {10}^{4}$ $\mathrm{kmph}$

4. $\frac{\mathrm{\pi}}{3}\times {10}^{4}$ $\mathrm{kmph}$

Subtopic: Kepler's Laws |

56%

From NCERT

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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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