Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The escape velocities of planet A and B are same. But A and B are of unequal mass.
Reason R: The product of their mass and radius must be same, `M_(1)R_(1)=M_(2)R_(2)`
In the light of the above statements, choose the most appropriate answer from the options given below :

Options

A. Both A and R are true but R is NOT the correct explanation of A
B. A is true but R is false
C. Both Statement I and Statement II are true
D. A is not correct but R is correct

Answer

To solve the problem, we need to analyze the given Assertion (A) and Reason (R) statements regarding the escape velocity of two planets.

### Step-by-Step Solution:

1. **Understanding Escape Velocity**:
The escape velocity \( v_e \) from the surface of 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 its radius.

2. **Analyzing Assertion A**:
The assertion states that the escape velocities of planets A and B are the same, but they have unequal masses.
- For two planets to have the same escape velocity, we can set their escape velocity equations equal to each other:
\[ \sqrt{\frac{2GM_A}{R_A}} = \sqrt{\frac{2GM_B}{R_B}} \]
Squaring both sides gives:
\[ \frac{2GM_A}{R_A} = \frac{2GM_B}{R_B} \]
Simplifying this leads to:
\[ \frac{M_A}{R_A} = \frac{M_B}{R_B} \]
This means that the ratio of mass to radius must be the same for both planets. Thus, Assertion A can be true if the ratio \( \frac{M}{R} \) is equal for both planets despite their unequal masses.

3. **Analyzing Reason R**:
The reason states that the product of their mass and radius must be the same, \( M_1 R_1 = M_2 R_2 \).
- This statement implies that the mass and radius of the two planets are directly proportional, which is not necessarily true. The correct condition derived from the escape velocity analysis is \( \frac{M_1}{R_1} = \frac{M_2}{R_2} \), not the product being equal.

4. **Conclusion**:
- Assertion A is true because it is possible for two planets of unequal mass to have the same escape velocity if their mass-to-radius ratios are equal.
- Reason R is false because it incorrectly states the condition for equal escape velocities.

### Final Answer:
- Assertion A is true.
- Reason R is false.