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 3v, then the speed of satellite B will be

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 3v, then the speed of satellite B will be (A)  3v/4  (B)  6v  (C)  12v  (D)  3v/2

Tardigrade Admin · Accepted Answer

Orbital velocity of satellite v=√(GM/r) ⇒ (vA/vB)=√(rB/rA)=√(R/4R)=(1/2) ∴ (vA/vB)=(3v/vB)=(1/2) ∴ vB=6v

Q. 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 3v, then the speed of satellite B will be

$3 v /4$

$6 v$

$12 v$

$3 v /2$

Orbital velocity of satellite $v = \frac{GM}{r}$ $\Rightarrow$ $\frac{v _{A}}{v _{B}} = \frac{r _{B}}{r _{A}} = \frac{R}{4 R} = \frac{1}{2}$ $∴$ $\frac{v _{A}}{v _{B}} = \frac{3 v}{v _{B}} = \frac{1}{2}$ $∴$ $v_{B} = 6 v$

Q. 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 3v, then the speed of satellite B will be

3v/4

6v

12v

3v/2

Orbital velocity of satellite v=rGM​​ ⇒ vB​vA​​=rA​rB​​​=4RR​​=21​ ∴ vB​vA​​=vB​3v​=21​ ∴ vB​=6v

$3 v /4$

$6 v$

$12 v$

$3 v /2$

Orbital velocity of satellite $v = \frac{GM}{r}$ $\Rightarrow$ $\frac{v _{A}}{v _{B}} = \frac{r _{B}}{r _{A}} = \frac{R}{4 R} = \frac{1}{2}$ $∴$ $\frac{v _{A}}{v _{B}} = \frac{3 v}{v _{B}} = \frac{1}{2}$ $∴$ $v_{B} = 6 v$