Ageiger–muller tube is a type of gas‑filled radiation detector. it can detect particles like x‑rays, alpha particles, and beta rays (electrons). this is useful in quantizing the activity of a radioactive source or determining if an area containing radioactive material is safe to enter. assuming that you have 1 mol of gas, if a geiger counter is filled with 9846 pa of argon gas at room temperature ( t = 21.1 °c ) , what is the density, rho , of the gas in this geiger tube?

Consider a double atwood machine constructed as follows: a mass 4m is suspended from a string that passes over a massless pulley on frictionless bearings. the other end of this string supports a second similar pulley, over which passes a second string supporting a mass of 3m at one end and m at the other. using two suitable generalized coordinates, set up the lagrangian and use the lagrange equations to find the acceleration of the mass 4m when the system is released. explain why the top pulley rotates even though it carries equal weights on each side.