If the escape velocity from the surface of Earth is denoted by \(v,\) then what would be the escape velocity from the surface of a planet whose mass is \(9\) times and radius is \(16\) times that of Earth?
1. \(\dfrac{v}{3}\) 2. \(\dfrac{2v}{3}\)
3. \(\dfrac{3v}{4}\) 4. \(\dfrac{9v}{4}\)
Subtopic:  Escape velocity |
 85%
Level 1: 80%+
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, the radius of Earth \(=6400~\text{km}\) )
1. \(1600~\text{km}\)
2. \(3200~\text{km}\)
3. \(6400~\text{km}\)
4. \(12800~\text{km}\)
Subtopic:  Escape velocity |
 64%
Level 2: 60%+
NEET - 2024
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The escape velocity of a body on the earth's surface is \(11.2~\text{km/s}.\) If the same body is projected upward with a velocity \(22.4~\text{km/s},\) the velocity of this body at an infinite distance from the centre of the earth will be:
1. \(11.2\sqrt2~\text{km/s}\)  2. zero
3. \(11.2~\text{km/s}\)  4. \(11.2\sqrt3~\text{km/s}\) 
Subtopic:  Escape velocity |
Level 3: 35%-60%
NEET - 2023
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The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and the same mass density is: 

1. \(3v\) 2. \(4v\)
3. \(v\) 4. \(2v\)
Subtopic:  Escape velocity |
 62%
Level 2: 60%+
NEET - 2021
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A particle of mass \(m\) is projected with a velocity, \(v=kv_{e} ~(k<1)\) from the surface of the earth. The maximum height, above the surface, reached by the particle is:
(Where \(v_e=\) escape velocity, \(R=\) the radius of the earth)

1. \(\dfrac{R^{2}k}{1+k}\) 2. \(\dfrac{Rk^{2}}{1-k^{2}}\)
3. \(R\left ( \dfrac{k}{1-k} \right )^{2}\) 4. \(R\left ( \dfrac{k}{1+k} \right )^{2}\)
Subtopic:  Escape velocity |
 64%
Level 2: 60%+
NEET - 2021
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The ratio of escape velocity at the Earth \((v_e)\) to the escape velocity at a planet \((v_p)\) whose radius and mean density are twice that of the Earth is:
1. \(1:2\sqrt{2}\)
2. \(1:4\)
3. \(1:\sqrt{2}\)
4. \(1:2\)
Subtopic:  Escape velocity |
 73%
Level 2: 60%+
NEET - 2016
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A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass\(m=5.98\times 10^{24}~\text{kg})\) have to be compressed to be a black hole?
1. \(10^{-9}~\text{m}\)
2. \(10^{-6}~\text{m}\)
3. \(10^{-2}~\text{m}\)
4. \(100​~\text{m}\)

Subtopic:  Escape velocity |
 63%
Level 2: 60%+
AIPMT - 2014
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The radius of a planet is twice the radius of the Earth. Both have almost equal average mass densities. If \(v_P\) and \(v_E\) are escape velocities of the planet and the earth, respectively, then:
1. \(v_P = 1.5 v_E\) 2. \(v_P = 2v_E\)
3. \(v_E = 3 v_P\) 4. \(v_E = 1.5v_P\)
Subtopic:  Escape velocity |
 78%
Level 2: 60%+
NEET - 2013
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A particle of mass \(m\) is kept at rest at a height \(3R\) from the surface of the Earth, where \(R\) is the radius of the Earth and \(M\) is the mass of the Earth. The minimum speed with which it should be projected, so that it does not return, is:
(where \(g\) is the acceleration due to gravity on the surface of the Earth)
1. \(\left(\dfrac{{GM}}{2 {R}}\right)^{\frac{1}{2}} \) 2. \(\left(\dfrac{{g} R}{4}\right)^{\frac{1}{2}} \)
3. \( \left(\dfrac{2 g}{R}\right)^{\frac{1}{2}} \) 4. \(\left(\dfrac{G M}{R}\right)^{\frac{1}{2}}\)
Subtopic:  Escape velocity |
 74%
Level 2: 60%+
NEET - 2013
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