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

Options

A. `(Delta R)/(2)sqrt((GM)/(R^(3))`
B. `-(DeltaR)/(4)sqrt((GM)/(R^(3))`
C. `Delta Rsqrt((GM)/(R^(3))`
D. `-Delta R sqrt((GM)/(R^(3))`

Answer

A

Explanation

`V = sqrt((GM)/(R ))=sqrt(GM) R^(-1//2)` ,bRlt `(dv)/(V)=-(1)/(2)(dR)/(R )`
put ` dV=Delta V, -dR=Delta R`
` Delta V=(V Delta R)/(2R),Delta V (sqrt((GM)/(R )))(Delta R)/(2R)`
` Delta V=(Delta R)/(2) sqrt((GM)/(R^(3))`