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
Answers
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
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Explanation:
v= √Gm\ r
3v\ vb = √r1\r2
= √ R\4R
=1/2
therefore 3v\ vb = 1/2
= 6v