Problem 1.377

A sphere moves with a relativistic velocity \(v\) through a gas whose unit volume contains \(n\) slowly moving particles, each of mass \(m\). Find the pressure \(p\) exerted by the gas on a spherical surface element perpendicular to the velocity of the sphere, provided that the particles scatter elastically. Show that the pressure is the same both in the reference frame fixed to the sphere and in the reference frame fixed to the gas.