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A set of 8 tuning forks is arranged in a  series of increasing order of frequencies.  Each fork gives 4 beats per second with  the next one and the frequency of last  fork is twice that of the first. Calculate  the frequencies of the first and the last  fork.
 Three particles of mass m each are placed at three corners of an equilateral triangle of side   a. The work, which should be done on this system to increase the sides of the triangle to   2a, is: