A cubic vessel (with face horizontal + vetical ) contains an ideal gas at NTP. The vessel is being carried by a rocket which is moving at a speed of `500 ms^(-1)` in vertical direction. The pressure of the gas inside the vessel as observed by us on the ground.

Options

A. remains the same because 500 `ms^(-1)` is very much smaller than `v_(rms)` of the gas
B. remains the same because motion of the vessel as a whole does not affect the relative motion of the gas molecules and the walls
C. will increase by a factor equal to `(v^(2)"_(rms)+(500)^(2))//v^(2)` where `v_(rms)` was the original mean squre velocity of the vessel
D. will be different on the top wall and bottom wall of the vessel

Explanation

To solve the problem, we need to analyze the situation of the cubic vessel containing an ideal gas under the influence of motion. The vessel is being carried by a rocket moving vertically at a speed of 500 m/s. We want to determine the pressure of the gas inside the vessel as observed from the ground.

### Step-by-Step Solution:

1. **Understand the Conditions**:
- The vessel is at Normal Temperature and Pressure (NTP), which means the gas is at a standard condition of temperature (0°C or 273.15 K) and pressure (1 atm or 101.3 kPa).
- The rocket is moving vertically at a speed of 500 m/s.

2. **Apply the Ideal Gas Law**:
- The pressure of an ideal gas can be expressed using the ideal gas equation:
\[ P = \frac{nRT}{V} \]
- Where \(P\) is the pressure, \(n\) is the number of moles of gas, \(R\) is the universal gas constant, \(T\) is the temperature, and \(V\) is the volume of the gas.

3. **Consider the Effects of Motion**:
- The vessel is moving with the rocket, but the gas molecules inside the vessel are still colliding with each other and with the walls of the vessel.
- The motion of the vessel does not affect the relative motion of the gas molecules with respect to the walls of the vessel.

4. **Collision Dynamics**:
- The gas molecules are in constant motion and collide elastically with each other and the walls of the vessel.
- The number of collisions per unit volume remains constant regardless of the vessel's motion.

5. **Conclusion on Pressure**:
- Since the number of moles, the volume of the vessel, and the temperature remain unchanged, and the collisions are unaffected by the vessel's motion, the pressure inside the vessel remains constant.
- Therefore, the pressure of the gas inside the vessel, as observed from the ground, remains the same as it was at NTP.

6. **Final Answer**:
- The pressure of the gas inside the vessel remains the same.