Two satellites A and B go around planet P in circular orbits having radius 4R and R respectively. If the speed of satellite A is 3 upsilon then the speed of satellite B will be :

Question

Two satellites A and B go around planet P in circular orbits having radius 4R and R respectively. If the speed of satellite A is 3 upsilon then the speed of satellite B will be : (A)  6 upsilon  (B)  9 upsilon  (C)  3 upsilon  (D) none of these

Tardigrade Admin · Accepted Answer

Orbital speed of sattelite upsilon =√(GM/r) ∴ ( upsilon 1/ upsilon 2)=√(r2/r1) (3 upsilon / upsilon 2)=√(R/4R)⇒ (3 upsilon / upsilon )=(1/2) upsilon 2=6 upsilon

Q. Two satellites A and B go around planet P in circular orbits having radius 4R and R respectively. If the speed of satellite A is $3 υ$ then the speed of satellite B will be :

$6 υ$

$9 υ$

$3 υ$

none of these

Orbital speed of sattelite $υ = \frac{GM}{r}$ $∴$ $\frac{υ _{1}}{υ _{2}} = \frac{r _{2}}{r _{1}}$ $\frac{3 υ}{υ _{2}} = \frac{R}{4 R} \Rightarrow \frac{3 υ}{υ} = \frac{1}{2}$ $υ_{2} = 6 υ$

Q. Two satellites A and B go around planet P in circular orbits having radius 4R and R respectively. If the speed of satellite A is 3υ then the speed of satellite B will be :

6υ

9υ

3υ