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1. | \(U > mgh\) |

2. | \(U < mgh\) |

3. | \(U = mgh\) |

4. | \(h,\) considered relative to the radius of the earth. | any of the above may be true depending on the value of

Subtopic: Gravitational Potential Energy |

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What should be the mass of a uniform sphere of radius \(R\) so that the escape velocity from its surface equals \(c,\) the velocity of light in vacuum? (Assume Newton's theory of gravitation to hold true)

1. | \(\dfrac{Rc^2}{G}\) | 2. | \(\dfrac{Rc^2}{2G}\) |

3. | \(\dfrac{2Rc^2}{G}\) | 4. | \(\sqrt2\dfrac{Rc^2}{G}\) |

Subtopic: Escape velocity |

81%

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A satellite is in a circular orbit around a planet, orbiting with a speed of \(2\) km/s. What is the minimum additional velocity that should be given to it, perpendicular to its motion, so that it escapes?

1. | \(2\) km/s | 2. | \(2\sqrt2\) km/s |

3. | \(2(\sqrt2-1)\) km/s | 4. | \(2(\sqrt2+1)\) km/s |

Subtopic: Escape velocity |

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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 |

80%

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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:

1. | \((4)^2T\) | 2. | \((4)^{\frac13}T\) |

3. | \(2T\) | 4. | \(8T\) |

Subtopic: Kepler's Laws |

63%

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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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Assume that a space shuttle flies in a circular orbit very close to the earth's surface. Taking the radius of the space shuttle's orbit to be equal to the radius of the earth (\(R\)) and the acceleration due to gravity to be \(g\), the time period of one revolution of the space shuttle is (nearly):

1. | \(\sqrt\frac{2R}{g}\) | 2. | \(\sqrt\frac{\pi R}{g}\) |

3. | \(\sqrt\frac{2\pi R}{g}\) | 4. | \(\sqrt\frac{4\pi^2 R}{g}\) |

Subtopic: Satellite |

69%

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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 |

84%

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Two satellites A and B move around the earth in the same orbit. The mass of B is twice the mass of A. Then:

1. | speeds of A and B are equal. |

2. | the potential energy of earth \(+\) A is same as that of earth \(+\) B. |

3. | the kinetic energy of A and B are equal. |

4. | the total energy of earth \(+\) A is same as that of earth \(+\) B. |

Subtopic: Satellite |

68%

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The time period of an earth satellite in circular orbit is independent of:

1. | the mass of the satellite |

2. | radius of the orbit |

3. | none of them |

4. | both of them |

Subtopic: Satellite |

78%

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