Match the following quantities related to satellite motion around Earth (mass M, radius R). List - I List - II (P) Ratio of kinetic energy to total mechanical energy for a satellite in a circular orbi

Question

Match the following quantities related to satellite motion around Earth (mass M, radius R).

List - I	List - II
(P) Ratio of kinetic energy to total mechanical energy for a satellite in a circular orbit.	(1) $24$
(Q) Minimum energy required to launch a satellite of mass 'm' from Earth's surface to a circular orbit of radius 2R.	(2) $- 1$
(R) Percentage increase in orbital velocity required for a satellite in a circular orbit of radius R to escape Earth's gravitational field.	(3) $\frac{3 GM m}{4 R}$
(S) Period of a geostationary satellite (in hours).	(4) $(2 - 1) \times 100%$

TestHub · Accepted Answer

P: For a satellite in circular orbit, K E = GM m / ( 2 r ) and TE = − GM m / ( 2 r ) . Ratio K E / TE = − 1 . Q: Initial energy on surface E i ​ = − GM m / R . Final energy in orbit at 2 R is E f ​ = − GM m / ( 2 × 2 R ) = − GM m / ( 4 R ) . Energy required = E f ​ − E i ​ = − GM m / ( 4 R ) − ( − GM m / R ) = 3 GM m / ( 4 R ) . R: Orbital velocity v o ​ = GM / R ​ . Escape velocity v e ​ = 2 GM / R ​ . Percentage increase = v o ​ v e ​ − v o ​ ​ × 100 = v o ​ ( 2 ​ − 1 ) v o ​ ​ × 100 = ( 2 ​ − 1 ) × 100% . S: A geostationary satellite has an orbital period equal to Earth's rotation period, which is 24 hours.

Physics - Gravitation Question with Solution | TestHub

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