Two satellite A and B go around the earth in circulaar orbits at a height of `R_A` and `R_B` respectively from the surface of the earth , Assume earth to be a uniform sphere of radius `R_e` . The ratio of the magnitude of the velocities of the satllilte `V_A/ V_B`

Options

A. `sqrtR_B/R_A`
B. `(R_s+ R_e)`/(`R_A+R_E)`
C. `(sqrt R_s+R_E)/(R_A +R_E)`
D. `(R_A/R_B)^2`

Answer

C

Explanation

Orbital velocity of satellite , `v_o=sqrt(GM_e)/(R_e+ R_B)`
For satellite Aand B,
`V_A= sqrt((GM_e)/(R_e+ R_A))` and `V_b = sqrt (GM_e)/(R_e+R_B)`
`therefore V_A/V_B=(sqrt(GM_e))/((R_e+R_A)/((GM_e)/(R_e+R_B)))`=`sqrt(R_e+R_B)/(R_e+R_A)`