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.

Options

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.

Answer

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.