Given below are two statements:
Statement I:For a planet, if the ration of mass of the planet toits radius increases, the escape velocity from the planet also increases.
Statement II : Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer from theoption given below

Options

A. Both Statement I and Statement II are incorrect
B. Both Statement I and Statement II are correct
C. Statement I is incorrect but Statement II is correct
D. Statement I is correct but Statement II is incorrect

Answer

To solve the problem, we need to analyze both statements regarding escape velocity and the relationship between mass, radius, and escape velocity of a planet.

### Step-by-Step Solution:

1. **Understanding Escape Velocity**:
The escape velocity (V_e) from a planet is given by the formula:
\[ V_e = \sqrt{\frac{2GM}{R}} \]
where \( G \) is the gravitational constant, \( M \) is the mass of the planet, and \( R \) is the radius of the planet.

2. **Analyzing Statement I**:
- Statement I claims that if the ratio of mass of the planet to its radius (M/R) increases, the escape velocity also increases.
- From the escape velocity formula, we can express it in terms of the ratio \( \frac{M}{R} \):
\[ V_e = \sqrt{2G \cdot \frac{M}{R}} \]
- If \( \frac{M}{R} \) increases, then \( V_e \) will also increase because \( V_e \) is directly proportional to \( \sqrt{\frac{M}{R}} \).
- Therefore, **Statement I is Correct**.

3. **Analyzing Statement II**:
- Statement II claims that escape velocity is independent of the radius of the planet.
- From the formula, we see that escape velocity is inversely proportional to the square root of the radius:
\[ V_e \propto \frac{1}{\sqrt{R}} \]
- This means that as the radius \( R \) increases, the escape velocity \( V_e \) decreases. Thus, escape velocity is dependent on the radius.
- Therefore, **Statement II is Incorrect**.

4. **Conclusion**:
- Statement I is correct, and Statement II is incorrect. Hence, the correct answer is that Statement I is true and Statement II is false.

### Final Answer:
- Statement I is correct.
- Statement II is incorrect.