Assertion (A) > : Two artificial satellites having different masses and revolving around the Earth in the same circular orbit have same speed. Reason (R) > : The speed of a satellite is directly proportional to the radius of its orbit.

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Q: 24 (NDA-I/2009)

Assertion (A) : Two artificial satellites having different masses and revolving around the Earth in the same circular orbit have same speed.
Reason (R) : The speed of a satellite is directly proportional to the radius of its orbit.

question_subject: 

Science

question_exam: 

NDA-I

stats: 

0,9,63,35,9,16,12

keywords: 

{'same circular orbit': [0, 0, 1, 0], 'artificial satellites': [0, 0, 1, 0], 'orbit': [0, 0, 1, 1], 'satellite': [0, 0, 0, 1], 'same speed': [0, 0, 1, 3], 'radius': [0, 0, 2, 2], 'different masses': [0, 0, 1, 0], 'speed': [0, 1, 2, 0]}

Option 1 states that both the assertion (A) and the reason (R) are true, and that the reason is the correct explanation for the assertion.

Assertion (A) states that two artificial satellites with different masses revolving around the Earth in the same circular orbit have the same speed. This is true because the speed of a satellite in an orbit only depends on the radius of its orbit and the mass of the Earth, not on the mass of the satellite itself.

Reason (R) states that the speed of a satellite is directly proportional to the radius of its orbit. This is also true because according to Kepler`s laws of planetary motion, the period of revolution (time taken to complete one orbit) is directly proportional to the radius of the orbit. Since the speed of the satellite is the distance traveled per unit time, a larger radius leads to a larger distance traveled in the same amount of time, resulting in a higher speed.

Therefore, both the assertion and the reason are true. However, the reason does not provide a correct explanation for the assertion. The speed of a satellite being directly proportional to the radius of its orbit does not directly explain why two satellites with different masses in the same circular orbit have the same speed. Hence, option 2 is the