A certain solenoid (50cm long with 2000 loops) carries a current of 0.7A and is in vacuum . An electron is shot at an angle of 10° to the solenoid axis from a point on the axis , what must be the speed of the electron if it is to just miss hitting the inside of the 1.6cm diameter solenoid.​

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.