Marina was immunized against chickenpox when she was young. Which of the following statements is true? Since she was immunized, it is impossible for Marina to contract chickenpox.
Marina was exposed to a weak form of chickenpox antigen.
The immunization provided Marina with passive immunity.
Marina needs to be immunized again because antibodies do not last long in the body.

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.