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1. | \(\dfrac{2 G m M}{3 R} \) | 2. | \(\dfrac{G m M}{2 R} \) |

3. | \(\dfrac{G m M}{3 R} \) | 4. | \( \dfrac{5 G m M}{6 R}\) |

Subtopic: Â Satellite |

From NCERT

NEET - 2024

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A rocket is fired vertically upward with a speed of \(\dfrac{v_e}{\sqrt2}\) from the earth's surface, where \(v_e\) is escape velocity on the surface of earth. The distance from the surface of earth upto which the rocket can go before returning to the earth is

(Given radius of earth \(=6400~\text{km}\) ):

(Given radius of earth \(=6400~\text{km}\) ):

1. | \(1600~\text{km}\) | 2. | \(3200~\text{km}\) |

3. | \(6400~\text{km}\) | 4. | \(12800~\text{km}\) |

Subtopic: Â Escape velocity |

Â 60%

From NCERT

NEET - 2024

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A body weighing \(100~\text{N}\) on the surface of earth weights \(x~\text{kg-ms}^{-2}\) at a height \(\dfrac{1}{9} R_E\) above the surface of earth. The value of \(x\) (\(g= 10~\text{ms}^{-2}\) at surface of earth and \(R_E\) is the radius of earth):

1. \(72\)

2. \(54\)

3. \(81\)

4. \(62\)

1. \(72\)

2. \(54\)

3. \(81\)

4. \(62\)

Subtopic: Â Acceleration due to Gravity |

Â 77%

From NCERT

NEET - 2024

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The mass of a planet is \(\left ( \dfrac{1}{10} \right )^{\text{th}} \) that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

1. | \(9.8 ~\text{ms}^{-2}\) | 2. | \(4.9 ~\text{ms}^{-2}\) |

3. | \(3.92 ~\text{ms}^{-2}\) | 4. | \(19.6~\text{ms}^{-2}\) |

Subtopic: Â Acceleration due to Gravity |

Â 62%

From NCERT

NEET - 2024

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The escape velocity for Earth is \(v.\) A planet having \(9\) times the mass of Earth and a radius, \(16\) times that of Earth, has the escape velocity of:

1. | \(\dfrac{v}{3}\) | 2. | \(\dfrac{2v}{3}\) |

3. | \(\dfrac{3v}{4}\) | 4. | \(\dfrac{9v}{4}\) |

Subtopic: Â Escape velocity |

Â 77%

From NCERT

NEET - 2024

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An object of mass \(100 ~\text{kg}\) falls from point \(A\) to \(B\) as shown in the figure. The change in its weight, corrected to the nearest integer is (\(R_E\) is radius of the earth):

1. \(49~\text N\)

2. \(89~\text N\)

3. \(5~\text N\)

4. \(10~\text N\)

1. \(49~\text N\)

2. \(89~\text N\)

3. \(5~\text N\)

4. \(10~\text N\)

Subtopic: Â Acceleration due to Gravity |

Â 56%

From NCERT

NEET - 2024

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If \(R\) is the radius of the earth and \(g\) is the acceleration due to gravity on the earth surface. Then the mean density of the earth will be:

1. | \(\dfrac{\pi RG}{12g}\) | 2. | \(\dfrac{3\pi R}{4gG}\) |

3. | \(\dfrac{3g}{4\pi RG}\) | 4. | \(\dfrac{4\pi G}{3gR}\) |

Subtopic: Â Acceleration due to Gravity |

Â 76%

From NCERT

NEET - 2023

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The escape velocity of a body on the earth's surface is \(11.2\) km/s. If the same body is projected upward with a velocity \(22.4\) km/s, the velocity of this body at infinite distance from the center of the earth will be:

1. | \(11.2\sqrt2\) km/s | 2. | zero |

3. | \(11.2\) km/s | 4. | \(11.2\sqrt3\) km/s |

Subtopic: Â Escape velocity |

From NCERT

NEET - 2023

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A satellite is orbiting just above the surface of the earth with period \(T.\) If \(d\) is the density of the earth and \(G\) is the universal constant of gravitation, the quantity \(\frac{3 \pi}{G d}\) represents:

1. \(\sqrt{T}\)

2. \(T\)

3. \(T^2\)

4. \(T^3\)

1. \(\sqrt{T}\)

2. \(T\)

3. \(T^2\)

4. \(T^3\)

Subtopic: Â Satellite |

Â 67%

From NCERT

NEET - 2023

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Two bodies of mass \(m\) and \(9m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be: (\(G\) = gravitational constant)

1. \(-\dfrac{20~Gm}{R}\)

2. \(-\dfrac{8~Gm}{R}\)

3. \(-\dfrac{12~Gm}{R}\)

4. \(-\dfrac{16~Gm}{R}\)

1. \(-\dfrac{20~Gm}{R}\)

2. \(-\dfrac{8~Gm}{R}\)

3. \(-\dfrac{12~Gm}{R}\)

4. \(-\dfrac{16~Gm}{R}\)

Subtopic: Â Gravitational Potential |

Â 52%

From NCERT

NEET - 2023

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