Question

The radii of circular orbits of two satellites A and B of the earth, are 4R and R, respectively. If the speed of satellite A is 3 V, then the speed of satellite B will be (a) 3 V/4 (b) 6 V (c) 12 V (d) 3 V/2 EBD_7179

Answer 1

Answer: option (b) 6v is correct choice.

let mass of satellite is m, mass of the earth is M

centripetal force = gravitational force between them,

⇒mv²/r = GMm/r²

⇒v = √{GM/r}

so, it is clear that velocity of satellite is inversely proportional to square root of radius of its circular orbit.

i.e., v ∝ 1/√r

now, v1/v2 = √(r2/r1)

given, v1 = 3v , r1 = 4R , r2 = R

so, 3v/v2 = √(R/4R) = 1/2

v2 = 6v

hence, speed of satellite B is 6v