Assertion : It we double the circular radius of a satellite, then its potential energy, kinetic energy and total mechanical energy will become half.
Reason : Orbital speed of a satellite.
`upsilon prop (1)/(sqrt(r )`
where, `r` is its radius of orbit.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explantion of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the problem, we need to analyze the assertion and the reason provided in the question step by step.

### Step 1: Understanding the Assertion
The assertion states that if we double the circular radius of a satellite, then its potential energy, kinetic energy, and total mechanical energy will become half.

### Step 2: Potential Energy Calculation
The gravitational potential energy (U) of a satellite in orbit is given by the formula:
\[ U = -\frac{GMm}{r} \]
where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth,
- \( m \) is the mass of the satellite,
- \( r \) is the radius of the orbit.

If we double the radius (i.e., \( r \) becomes \( 2r \)), the new potential energy \( U' \) will be:
\[ U' = -\frac{GMm}{2r} \]
This shows that the potential energy becomes half of the original potential energy:
\[ U' = \frac{U}{2} \]

### Step 3: Kinetic Energy Calculation
The kinetic energy (KE) of the satellite is given by:
\[ KE = \frac{1}{2} mv^2 \]
The orbital speed \( v \) is determined by the gravitational force providing the necessary centripetal force:
\[ mv^2 = \frac{GMm}{r^2} \]
This leads to:
\[ v^2 = \frac{GM}{r} \]
Thus, the kinetic energy becomes:
\[ KE = \frac{1}{2} m \left(\frac{GM}{r}\right) = \frac{GMm}{2r} \]

If we double the radius, the new speed \( v' \) becomes:
\[ v' = \sqrt{\frac{GM}{2r}} \]
The new kinetic energy \( KE' \) will be:
\[ KE' = \frac{1}{2} m \left(\frac{GM}{2r}\right) = \frac{GMm}{4r} \]
This shows that the new kinetic energy is also half of the original kinetic energy:
\[ KE' = \frac{KE}{2} \]

### Step 4: Total Mechanical Energy Calculation
The total mechanical energy (E) is the sum of potential and kinetic energy:
\[ E = U + KE \]
Substituting the expressions we derived:
\[ E = -\frac{GMm}{r} + \frac{GMm}{2r} \]
This simplifies to:
\[ E = -\frac{GMm}{2r} \]

When we double the radius, the total mechanical energy \( E' \) becomes:
\[ E' = -\frac{GMm}{2(2r)} = -\frac{GMm}{4r} \]
This shows that the total mechanical energy also becomes half of the original total mechanical energy:
\[ E' = \frac{E}{2} \]

### Conclusion
Thus, we have shown that when the radius is doubled:
- Potential energy becomes half,
- Kinetic energy becomes half,
- Total mechanical energy becomes half.

### Step 5: Analyzing the Reason
The reason states that the orbital speed of a satellite is inversely proportional to the square root of the radius:
\[ v \propto \frac{1}{\sqrt{r}} \]
This is indeed true, but it only explains the kinetic energy becoming half. It does not explain why the potential and total mechanical energy also become half.

### Final Answer
Both the assertion and the reason are true, but the reason is not the correct explanation for the assertion.