A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R, `h lt lt R`). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to :(Neglect the effect of atmosphere.)

Options

A. `sqrt(gR//2)`
B. `sqrt(gR) (sqrt(2) - 1)`
C. `sqrt(2gR)`
D. `sqrt(gR)`

Answer

B

Explanation

For h `lt lt ` R, the orbital velocity is `sqrt(gR)`
Escape velocity = `sqrt(2gR)`
`therefore` The minimum increase in its orbital velocity
` = sqrt(2gR) - sqrt(gR) = sqrt(gR) ( sqrt(2) - 1 ) `