As we know
v= underroot 3P upon rho
and v=c as per question
now we get
c= underroot 3P by Rho
now squaring on both side we get
c^2=3P By rho
By this equation find P which will be
P=c^2 × rho divided by 3
hope it will help

Pressure exerted by a moving gas

Pressure is defined as the force exerted per unit area. In the case of a gas, pressure is caused by the collision of gas molecules with the walls of the container. When the gas as a whole moves with a velocity V, the pressure exerted by the gas is affected by this motion.

Effect of motion on gas molecules

When the gas as a whole moves with a velocity V, the individual gas molecules also acquire this velocity. The motion of gas molecules can be described by their root mean square velocity (c), which represents the average speed of the molecules.

Deriving the expression for pressure

To determine the pressure exerted by the gas, we can consider a small area on the wall of the container. The gas molecules that collide with this area exert a force on it due to their motion. The force exerted by each molecule can be calculated using Newton's second law (F = ma), where m is the mass of the molecule and a is its acceleration.

The acceleration of a gas molecule can be expressed as a = (change in velocity / time taken). Since the motion of gas molecules is random, the change in velocity is given by Δv = 2c, where c is the root mean square velocity.

The time taken for a molecule to collide with the wall can be approximated as the time taken for the molecule to travel the distance between the molecules, which is equal to the average distance between the molecules divided by the root mean square velocity (Δx / c).

Therefore, the acceleration of the gas molecule can be written as a = (2c / Δx) * c = (2c^2 / Δx).

Calculating the force and pressure

The force exerted by a single molecule can be calculated as F = ma = m * (2c^2 / Δx).

The pressure exerted by the gas on the wall can be obtained by summing up the forces exerted by all the gas molecules and dividing by the area of the wall. Since the gas is assumed to be in equilibrium, the pressure is the same in all directions.

P = (ΣF) / A = (Σ(m * 2c^2 / Δx)) / A,

where Σ represents the sum over all gas molecules and A is the area of the wall.

Conclusion

In conclusion, when a gas moves as a whole with a velocity V, the pressure exerted by the gas is affected by the motion. The pressure is determined by the forces exerted by individual gas molecules due to their motion. By considering the change in velocity, the time taken for collisions, and summing up the forces exerted by all the gas molecules, we can calculate the pressure exerted by the gas.