Ametal ring of radius a and mass m falls into a constant and uniform gravitational field, with the acceleration g, inside a magnetic field, in which the vertical component bz depends on z. the plane of the ring remains horizontal and the resistance of the ring is r. if the inductance of the ring is negligible, prove that for a long fall, the ring's velocity becomes independent of z if (dbz/dz) → b1 for large |z|, where b1 is a constant. find this constant limiting velocity. find the velocity at all times for the case bz = b0 + b1z, where b0 and b1 are constants.

The frequency of a tuning fork can be found by the method shown. a long tube open at both ends is submerged in a beaker of water, and the vibrating tuning fork is placed near the top of the tube. the length l of the air column is adjusted by moving the tube vertically. the sound waves generated by the fork are reinforced when the length of the air column corresponds to one of the resonant frequencies of the tube. the smallest value for l for which a peak occurs in sound intensity is 7 cm. l what is the frequency of the tuning fork? the speed of sound in air is 345 m/s. answer in units of hz