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Assertion : Orbital velocity of a sate...

Assertion : Orbital velocity of a satellite is greater than its escape velocity.
Reason : Orbit of a satellite is within the gravitational field of earth whereas escaping is beyond the gravitational field of earth.

A

Assertion is correct, reason is correct, reason is a correct explanation for assertion.

B

Assertion is correct, reason is correct, reason is not a correct explanation for assertion

C

Assertion is correct, reason is incorrect

D

Assertion is incorrect, reason is correct

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding Orbital Velocity**: - The orbital velocity of a satellite is the speed required for it to maintain a stable orbit around a celestial body (like Earth). This velocity depends on the mass of the celestial body and the radius of the orbit. - Formula: \( v_o = \sqrt{\frac{GM}{r}} \) where \( G \) is the gravitational constant, \( M \) is the mass of the celestial body, and \( r \) is the distance from the center of the celestial body to the satellite. 2. **Understanding Escape Velocity**: - The escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any further propulsion. - Formula: \( v_e = \sqrt{2GM/r} \) - This means that escape velocity is always greater than orbital velocity. 3. **Comparing the Two Velocities**: - From the formulas, we can see that: \[ v_e = \sqrt{2} \cdot v_o \] - This indicates that escape velocity (\( v_e \)) is greater than orbital velocity (\( v_o \)). 4. **Analyzing the Assertion**: - The assertion states that "the orbital velocity of a satellite is greater than its escape velocity." This is incorrect based on our calculations. 5. **Analyzing the Reason**: - The reason states that "the orbit of a satellite is within the gravitational field of Earth whereas escaping is beyond the gravitational field of Earth." - This statement is true, as a satellite in orbit is indeed within the gravitational influence of Earth, while escape velocity refers to moving beyond this influence. 6. **Conclusion**: - Since the assertion is false and the reason is true, the correct answer is that the assertion is incorrect but the reason is correct. ### Final Answer: - The assertion is false, and the reason is true. Therefore, the correct option is that the assertion is incorrect, and the reason is correct.
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