NEETPhysicsGravitation
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Two satellites of masses m and 4m orbiting the Earth in the same circular orbit have the same time period. Reason (R): The time period of a satellite in a circular orbit is directly proportional to its own mass. In the light of the above statements, choose the most appropriate answer from the optio
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
C. (A) is true but (R) is false
Step-by-step solution
The time period of a satellite in a circular orbit of radius R around the Earth (mass M ) is given by: T = 2 R^3 GM This formula shows that the time period depends only on the mass of the central body ( M ) and the orbital radius ( R ). It is completely independent of the mass of the satellite ( m ). Therefore, two satellites of different masses ( m and 4m ) in the exact same orbit will have the same time period. Thus, Assertion (A) is true. Since the time period is independent of the satellite's mass, Reason (R) i