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Statemet-1: Two satellites A & B are in ...

Statemet-1: Two satellites A & B are in the same orbit around the earth B being behind A. B cannot overtake A by increasing its speed.
Statement-2: it will then go into a different orbit.

A

Statement-1 is true, statement-2 is true: Statement-2 is a correct explanation for statement-1

B

Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1

C

Statement-1 is true, Statement-2 is false.

D

Statement-1 is false, Statement-2 is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze both statements regarding the satellites A and B in orbit around the Earth. ### Step 1: Understanding the Orbit of Satellites Satellites in the same orbit have the same orbital radius and speed. The orbital speed \( v \) of a satellite is given by the formula: \[ v = \sqrt{\frac{GM}{r}} \] where \( G \) is the gravitational constant, \( M \) is the mass of the Earth, and \( r \) is the radius of the orbit. ### Step 2: Analyzing Statement 1 Statement 1 claims that satellite B cannot overtake satellite A by increasing its speed. If satellite B tries to increase its speed while remaining in the same orbit, it will not be able to maintain that orbit because the orbital speed is fixed for a given radius. ### Step 3: Analyzing Statement 2 Statement 2 states that if satellite B increases its speed, it will go into a different orbit. This is true because increasing the speed of a satellite results in a decrease in the radius of its orbit, according to the relationship between speed and radius. Therefore, if B increases its speed, it will move to a lower orbit. ### Step 4: Conclusion on Statements Both statements are true: - Statement 1 is true because B cannot overtake A by merely increasing its speed in the same orbit. - Statement 2 is true because increasing speed leads to a change in orbit. ### Step 5: Relationship Between Statements Statement 2 correctly explains Statement 1. Since increasing the speed of satellite B causes it to enter a different orbit, it cannot overtake satellite A in the same orbit. ### Final Answer Both statements are true, and Statement 2 is the correct explanation of Statement 1.
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