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Q. No.The escape velocity of a particle of mass \(m\) varies as:
| 1. | \(m^{2}\) | 2. | \(m\) |
| 3. | \(m^{0}\) | 4. | \(m^{-1}\) |
Subtopic: Â Escape velocity |
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The value of acceleration due to gravity on the surface of a planet is \(\left ( \dfrac{1}{6} \right )\)th that of the earth. The radius of the planet is \(\left ( \dfrac{1}{3} \right )\)rd of earth's radius. What is the escape speed from the surface of the planet?
(Given the escape from the surface of earth is \(v_{e}\) km/s)
(Given the escape from the surface of earth is \(v_{e}\) km/s)
| 1. | \(\sqrt{\dfrac{1}{18}} v_e\) | 2. | \(\sqrt{\dfrac{1}{2}} v_e\) |
| 3. | \(\sqrt{\dfrac{1}{9}} v_e\) | 4. | \(\sqrt{\dfrac{1}{10}} v_e\) |
Subtopic: Â Escape velocity |
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The escape speed of a projectile on the earth's surface is nearly \(11\) km/s. A body is projected out from earth at twice this speed. What is the speed of the body far away from the earth?
(Ignore the presence of the sun and other planets.)
(Ignore the presence of the sun and other planets.)
| 1. | \(\sqrt{200}\) km/s | 2. | \(\sqrt{250}\) km/s |
| 3. | \(\sqrt{300}\) km/s | 4. | \(\sqrt{363}\) km/s |
Subtopic: Â Escape velocity |
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For a satellite, the escape velocity is \(11.2\) km/s from the surface of the earth. If the satellite is launched at an angle of \(60^\circ\) with the vertical, then the escape velocity will be:
| 1. | \(11.2 ~\cos60^\circ\) km/s | 2. | \(11.2 ~\sin60^\circ\) km/s |
| 3. | \(11.2\) km/s | 4. | \(11.2 ~\tan60^\circ\) km/s |
Subtopic: Â Escape velocity |
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A planet has a radius twice but density \(\dfrac14\) as compared to earth. The ratio of escape velocity from earth to that from the planet will be:
| 1. | \(1:2\) | 2. | \(1:1\) |
| 3. | \(2:1\) | 4. | \(3:1\) |
Subtopic: Â Escape velocity |
 82%
From NCERT
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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: Â Escape velocity |
From NCERT
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: Â Escape velocity |
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From NCERT
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, \(R=\) radius of the earth)
| 1. | \(\frac{R^{2}k}{1+k}\) | 2. | \(\frac{Rk^{2}}{1-k^{2}}\) |
| 3. | \(R\left ( \frac{k}{1-k} \right )^{2}\) | 4. | \(R\left ( \frac{k}{1+k} \right )^{2}\) |
Subtopic: Â Escape velocity |
 59%
From NCERT
NEET - 2021
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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. \(12800~\text{km}\)
(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: Â Escape velocity |
 65%
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 |
 81%
From NCERT
NEET - 2024
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