Assertion : If radius of earth suddenly shrinks to half its present without changing its mass value, then the period of an earth's satellite will not change
Reason : Time period of a satellite does not upon the mass of earth.

Options

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

Explanation

To solve the question, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that if the radius of the Earth shrinks to half its present size without changing its mass, the period of an Earth satellite will not change.

### Step 2: Recall the Formula for the Time Period of a Satellite
The time period \( T \) of a satellite in orbit is given by the formula:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]
where:
- \( T \) is the time period of the satellite,
- \( r \) is the radius of the orbit of the satellite,
- \( G \) is the gravitational constant,
- \( M \) is the mass of the Earth.

### Step 3: Analyze the Effect of Changing Earth's Radius
In the assertion, the radius of the Earth changes, but we need to determine if this affects the time period of the satellite. The key point is that the formula for the time period depends on the radius of the satellite's orbit \( r \) and the mass of the Earth \( M \), but not on the radius of the Earth itself.

Since the radius of the Earth does not appear in the formula for the time period, even if the Earth’s radius shrinks to half, the time period \( T \) will remain unchanged as long as the mass \( M \) of the Earth remains constant.

### Conclusion for the Assertion
Thus, the assertion is **true**: the period of an Earth satellite will not change if the radius of the Earth shrinks to half without changing its mass.

### Step 4: Analyze the Reason
The reason states that the time period of a satellite does not depend on the mass of the Earth. This statement is incorrect. The time period \( T \) is indeed dependent on the mass of the Earth \( M \) because it appears in the denominator of the formula. Specifically, the time period is inversely proportional to the square root of the mass of the Earth.

### Conclusion for the Reason
Therefore, the reason is **false**: the time period of a satellite does depend on the mass of the Earth.

### Final Conclusion
- The assertion is true.
- The reason is false.

Thus, the correct answer is that the assertion is true, but the reason is false.

---