NEETPhysicsGravitation
A planet of mass M, has two natural satellites with masses m 1 a n d m 2 . The radii of their circular orbits are R 1 a n d R 2 respectively. Ignore the gravitational force between the satellites. Define v 1 , L 1 , K 1 a n d T 1 to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1 ; a n d v 2 , L 2 , K 2 a n d T 2 and to be the corresponding quantities
Options
- Aa-p;b-q;c-s;d-r;
- Ba-s;b-p;c-r;d-q;
- Ca-s;b-q;c-r;d-p;
- Da-r;b-q;c-s;d-p;
Correct answer
D. a-r;b-q;c-s;d-p;
Step-by-step solution
m 1 m 2 = 2 R 1 R 2 = 1 4 given G M m 1 R 1 2 = m 1 V 1 1 R 1 v 1 2 = G M R 1 , v 2 2 = G M R 2 v 1 2 v 2 2 = R 2 R 1 = 4 i v 1 v 2 = 2 i i L = m v R L 1 L 2 = m 1 v 1 R 1 m 2 v 2 R 2 = 2 × 2 × 1 4 = 1 i i i K = 1 2 m v 2 K 1 K 2 = m 1 v 1 2 m 2 v 2 2 = 2 × 2 2 = 8 ( i v ) T = 2 π R / V T 1 T 2 = R 1 v 1 × v 2 R 2 = R 1 R 2 × v 2 v 1 = 1 4 × 1 2 = 1 8