Assertion : If the projuct of surface area and density is same for both planets, escape velocity will be same for both.
Reason : Product of surface area and density is proportional to the mass of the planet per unit radius of the planet.

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 both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states: "If the product of surface area and density is the same for both planets, escape velocity will be the same for both."

- Escape velocity (Ve) 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.

### Step 2: Relate Surface Area and Density to Mass
The surface area \( A \) of a planet can be expressed as:
\[ A = 4\pi R^2 \]
The density \( \rho \) is defined as mass per unit volume. The volume \( V \) of a sphere is:
\[ V = \frac{4}{3}\pi R^3 \]
Thus, the mass \( M \) can be expressed as:
\[ M = \rho V = \rho \left(\frac{4}{3}\pi R^3\right) \]

### Step 3: Calculate the Product of Surface Area and Density
Now, we calculate the product of surface area and density:
\[ A \cdot \rho = (4\pi R^2) \cdot \rho = 4\pi R^2 \cdot \rho \]
Substituting for \( M \):
\[ A \cdot \rho = 4\pi R^2 \cdot \left(\frac{3M}{4\pi R^3}\right) = 3\frac{M}{R} \]
This shows that the product of surface area and density is proportional to the mass of the planet per unit radius.

### Step 4: Analyze the Escape Velocity
Since we have established that the product of surface area and density is proportional to \( \frac{M}{R} \), we can see that if this product is the same for two planets, then:
\[ \frac{M_1}{R_1} = \frac{M_2}{R_2} \]
This implies that the escape velocities for both planets will be the same, as they depend on the ratio of mass to radius.

### Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer
Both assertion and reason are correct, and the reason is the correct explanation of the assertion.

---