A satellite is revolving round the earth at a height (R/2) from surface of earth in circular orbit. The change ini speed required for the satellite to excape to infinity for the satellite to escape to infinity is: [Take R as radius of earth and M as mass of earth]

Options

A. `sqrt((2GM)/(3R))`
B. `sqrt((GM)/(3R))(2-sqrt(2))`
C. `sqrt((GM)/(3R))(sqrt(2)-1)`
D. `sqrt((4GM)/(3R))`

Answer

B

Explanation

`V_(0)=sqrt((GM)/(3R//2))=sqrt((2GM)/(3R))`
in order to escape to infinity let `(V-V_(0))` is te speed change required thus
`(-GMm)/((3R//2))+(1)/(2)m(v)^(2)=0`
thus, `V=sqrt((4GM)/(3R))`
thus speed change required `=v-v_(0)`
`DeltaV=sqrt((4GM)/(3R))-sqrt((2GM)/(3R)),DeltaV=sqrt((GM)/(3R))(2-sqrt(2))`