A space station is at a height equal to the radius of the Earth . If `v_E` is the escape velocity on the surface of the Earth , the same the spastation `v_E`

Options

A. `1/2`
B. `1/4`
C. `1/sqrt2`
D. `1/sqrt3`

Answer

C

Explanation

The escape velocity on the surface of the Earth is
`v_E=sqrt((2GM)/R)`
where M and R are the mass and radius of the Earth respectively.
As the space station is at a height h from the surface of the earth , its distance form the centre of the earth is (R+h).
Thus, the escape velocity on the space station is
`v_S=sqrt((2GM)/((R+h)))=sqrt((2GM)/((R+h)))=sqrt((2GM)/(2R))=(as h = R)`
`=1/sqrt2(sqrt((2GM)/R))=(v_E)/sqrt2`