If due to air drag, the orbital radius of satelite decreases from R to `R-DeltaR,DeltaRltltR`, then the expression for change is orbital velocity `Deltav` is [mass of earth M]:-

Options

A. `(DeltaR)/(2) sqrt((GM)/(R^(3)))`
B. `-(DeltaR)/(2) sqrt((GM)/(R^3))`
C. `DeltaRsqrt((GM)/(R^(3)))`
D. `-DeltaRsqrt((GM)/(R^(3)))`

Answer

A

Explanation

`V=sqrt((GM)/(R))=sqrt(GM) R^(-1//2)`
`(DeltaV)/(V)=-(1)/(2)(DeltaR)/(R) necaise DeltaRrarrDeltaR`
`DeltaV=sqrt((GM)/(R))(DeltaR)/(2R)`
`DeltaV=sqrt((GM)/(R^(3)).(DeltaR)/(2)`