Question

A planet of mass M, has two natural satellites with
masses ml and m2. The radii of their circular orbits
are R, and R, respectively. Ignore the provisional
force between the satellites Define v.LK, and
T to be, respectively, the orbital speed, angularmo
mentum, kinetic energy and time period of revolu.
tion of satellite 1: and v, L. Kand T. to be the
corresponding quantities of satellite 2.Given m/m,
-2 and R/R-1/4, match the ratios in List Ito
the numbers in List-II. ​

Answer 1

Answer:

planet of mass M, has two natural satellites with masses m1 and m2. The radii of their circular orbits are R1 and R2 respectively. Ignore the gravitational force between the satellites. Define v1, L1, K1 and T1 to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and v2, L2, K2 and T2 to be the corresponding quantities of satellite 2. Given m1/m2 = 2 and R1/R2 = 1/4, match the ratios in List-I to the numbers in List-II. List–I List–II P. v1/v2 1. 1/8 Q. L1/L2 2. 1 R K1/K2 3. 2 S T1/T2 4. 8 (A) P → 4 ; Q → 2 ; R → 1 ; S → 3 (B) P → 3 ; Q → 2 ; R → 4 ; S → 1 (C) P → 2 ; Q → 3 ; R → 1 ; S → 4 (D) P → 2 ; Q → 3 ; R → 4 ; S → 1Read more on Sarthaks.com - https://www.sarthaks.com/61378/a-planet-of-mass-m-has-two-natural-satellites-with-masses-m1-and-m2

Answer 2

GMm1R21=m1v21R1  

v21=GMR1,v22=GMR2

v21v22=R2R1=4

(P) v1v2=2

(Q) L=mvR

L1L2=m1v1R1m2v2R2=2×2×14=1

(R) K=12mv2

K1K2=m1v21m2v22=2×(2)2=8

(S) T=2πR/V

T1T2=R1V1×v2R2=R1R2×v2v1=14×12=18