A wire must be replaced in a circuit by a new wire of the same material but nine times longer. If the new wire's resistance is the same as the original wire's, what is the diameter of the new wire?

O the same as the original diameter
O one half the original diameter
O one third the original diameter
O three times the original diameter
O nine times the original diameter

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.