A space station is set up in space at a distance equal to the earth’s radius from the surface of the earth. Suppose a satellite can be launched from the space station. Let $v_{1}$ and $v_{2}$ be the escape velocities if the satellite on the earth’s surface and space station, respectively. Then,

v_{2} = v_{1}

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v_{2} < v_{1}

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v_{2} > v_{1}

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(a), (b) and (c) are valid depending on satellite.

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Solution

The correct option is B $v_{2} < v_{1}$

$v_{1} = \sqrt{\frac{2 G M}{R}}$
By energy conservation for satellite launched from space station,
$v_{2} = \sqrt{\frac{G M}{R}}$
$v_{2} = \sqrt{2} v_{2}$

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A space station is set up in space at a distance equal to the earth’s radius from the surface of the earth. Suppose a satellite can be launched from the space station. Let v1 and v2 be the escape velocities if the satellite on the earth’s surface and space station, respectively. Then,

The correct option is B v2<v1 v1=√2GMR By energy conservation for satellite launched from space station, v2=√GMR v2=√2v2

A space station is set up in space at a distance equal to the earth’s radius from the surface of the earth. Suppose a satellite can be launched from the space station. Let $v_{1}$ and $v_{2}$ be the escape velocities if the satellite on the earth’s surface and space station, respectively. Then,

The correct option is B $v_{2} < v_{1}$

$v_{1} = \sqrt{\frac{2 G M}{R}}$
By energy conservation for satellite launched from space station,
$v_{2} = \sqrt{\frac{G M}{R}}$
$v_{2} = \sqrt{2} v_{2}$