If ` v_(0)` be the orbital velocity of a satellite in a circular orbit close to the earth's surface and `v_(e)` is the escape velocity from the earth , then relation between the two is

Options

A. `v_(0)=v_(e)`
B. `v_(e)=sqrt(3)v_(0)`
C. `v_(e)=sqrt(2)v_(0)`
D. `v_(e)=2v_(0)`

Answer

C

Explanation

Orbital velocity of satellite ` =v_(o)` and escape velocity from the earth ` =v_(e)` .
We have orbital velocity ` (v_(0))=sqrt(gR)` and escape velocity ` (v_(e))=sqrt(2 gR )`
Therefore ratio of orbital velocity to escape velocity `(v_(o))/(v_(e))=sqrt((gR)/(2gR))=(1)/(sqrt(2)) or v_(2)= sqrt(2)v_(o)` .