Two satellities `s_(1)` a & `s_(2)` of equal masses revolves in the same sense around a heavy planet in coplaner circular orbit of radii `R` & `4R`

Options

A. the ratio of period of revolution `s_(1)` & `s_(2)` is `1 : 8`.
B. their velocities are in the ratio `2 : 1`
C. their angular momentum about the planet are in the ratio `2 : 1`
D. the ratio of angular velocities of `s_(2)` w.r.t. `s_(1)` when all three are in the same line is `9 : 5`.

Answer

A, B, D

Explanation

`T= 2pi sqrt((r^(3))/(GM))rArr (T_(1))/(T_(2))=((1)/(4))^(3//2)rArr(T_(1))/(T_(2))=(1)/(8)`
(B) `V=sqrt((GM)/(r )) rArrr (V_(1))/(V_(2)) = ((4)/(1))^(1//2)rArr (V_(1))/(V_(2))=(2)/(1)`
(C )`(L_(1))/(L_(2)) = (mV_(1)R)/(mV_(2)(4R))rArr (L_(1))/(L_(2))=(2)/(1)xx(1)/(4) rArr (L_(1))/(L_(2))=(1)/(2)`
So option (A) (B) and (D) are correct choice.