A : Magnitude of mean velocity of the gas molecules is same as their mean speed.
R : The only difference between mean velocity and mean speed is that mean velocity is a vector and mean speed is a scalar.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then Mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To solve the assertion and reason problem, we will analyze both statements step by step.

### Step 1: Analyze the Assertion
The assertion states that "the magnitude of mean velocity of the gas molecules is the same as their mean speed."

- **Mean Velocity**: This is a vector quantity that takes into account both the magnitude and direction of the gas molecules' motion. In a gas, molecules move randomly in all directions.
- When we calculate the mean velocity of gas molecules, we sum the velocities of all the molecules. Due to their random motion, the positive and negative components of their velocities will cancel each other out, leading to a mean velocity of zero.

- **Mean Speed**: This is a scalar quantity that only considers the magnitude of the velocities of the gas molecules, ignoring their direction. The mean speed is always a positive value since it is the average of the absolute values of the velocities.

Thus, the assertion is **false** because the magnitude of mean velocity (which is zero) is not the same as the mean speed (which is a positive value).

### Step 2: Analyze the Reason
The reason states that "the only difference between mean velocity and mean speed is that mean velocity is a vector and mean speed is a scalar."

- While it is true that mean velocity is a vector and mean speed is a scalar, this statement oversimplifies the difference between the two.
- As established earlier, the mean velocity of gas molecules is zero due to the cancellation of their random directions, while the mean speed is a non-zero value reflecting the average of their speeds.

Therefore, the reason is also **false** because it does not accurately describe the significant difference in the magnitudes of mean velocity and mean speed.

### Conclusion
Since both the assertion and the reason are false, the final answer is that both the assertion (A) and the reason (R) are false.

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