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 of the satellite on the earth's surface and space station, respectively. Then

Options

A. `v_(2)=v_(1)`
B. `v_(2)ltv_(1)`
C. `v_(2)gtv_(1)`
D. a,b and c are valid depending on the mass of satellite

Answer

B

Explanation

From surface of the earth, the escape velocity is `sqrt((2GM)//R)`
From the satellite the escape velocity is caculated as follows.
`1/2mv_(2)^(2)-(GMm)/(2R)=0`
`impliesv_(2)^(2)=sqrt((GM)/R)impliesv_(2)ltv_(1)`