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 \(=6400~\text{km}\) ):
1. \(1600~\text{km}\) 2. \(3200~\text{km}\)
3. \(6400~\text{km}\) 4. \(12800~\text{km}\)
Subtopic:  Escape velocity |
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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:  Escape velocity |
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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:  Escape velocity |
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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 |
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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. \(\dfrac{R^{2}k}{1+k}\) 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 |
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