Consider three identical metal spheres, A, B, and C. Sphere A carries a charge of +7q. Sphere B carries a charge of – 2q. Sphere C carries no net
charge. Spheres A and B are touched together and then separated.
Sphere C is then touched to sphere A, and separated from it. Last, sphere
C is touched to sphere B and separated from it. (a) How much charge
ends up on sphere C? What is the total charge on the three spheres (b)
before they are allowed to touch each other and (c) after they have
touched?

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.