If `v_(e)` is escape velocity and `v_(0)`, is orbital velocity of satellite for orbit close to the earth's surface. Then are related by

Options

A. `v_0 = sqrt(2v_e)`
B. `v_0= v_e `
C. `v_e = sqrt(2v_0)`
D. `v_e =sqrt2v_0`

Answer

D

Explanation

Escape velocity, `v_e = sqrt((2GM)/( R) ) ` ....(i)
where M and R be the mass and radius of the earth respectively. The orbital velocity of a satellite close to the earth.s surface is
`v_0 = sqrt((GM)/( R)) ` .....(ii)
From (i) and (ii), we get
` v_e = sqrt2 v_0`