Freak with Frequency

Electricity and Magnetism Level 4

In the problem a figure is shown a figure which consist of a mass m=10 kg attached to a string on smooth table whose other end through a very tiny hole in the table is attached to a another mass M=1 kg in the shape of a block attached to a rod of length 1metre.When M is in equilibrium m is rotating on the table with a angular frequency 1radian/sec with a radius r=1metre about the hole. The rod can slide on the a set of vertical smooth parallel conducting rails fixed as shown.There exists a magnetic field B which we can change perpendicular to the plane of the rails. The rails are also attached to a inductor L=1H whose two ends are connected to a circuit given in the figure.The circuit contains another two inductors which are identical but whose inductance is unknown ,a capacitor whose capacitance is unknown and a bulb. In front of the bulb is a Frequency Detector connected to a Electric field generator which generated a uniform electric field E directly proportional to the angular frequency detected by the frequency detector.At time t=0 we release from the same height in the uniform electric field two neutral conducting metal balls. assume that the electric field exists even very below the ball. the metal balls are very small of radius r and mass m and are connected with a very light conducting inextensible thread of length b=2 metres .Initial separation of the balls is a=1meter. Initially M is in equilibrium and m is rotating no current flows anywhere . We displace the (rod and mass)M by a very small distance and release it at t=0 The bulb now is dimmest. the conducting balls attain their maximum horizontal velocity U at some time.

Now we again do this experiment starting from equilibrium by changing the magnetic field so that the bulb is brightest.Now the conducting balls attain a maximum horizontal velocity V at another certain time.Find V-U \[E=K\omega,K=10^{12}SIunits\] Assume\[r\ll a\] \[r=\frac{\varepsilon}{\pi}metres\]

\[B=3^{0.5}T\] at dimmest

the whole experiment setup is carried out at a good distance above the ground.


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