Q. 19

A bar magnet of magnetic moment m and moment of inertia I (about center, perpendicular to length) is cut into two equal pieces, perpendicular to length. Let T be the period of oscillations of the original magnet about an axis through the mid-point, perpendicular to length, in a magnetic field B. What would be the similar period T’ for each piece?

Answer :

Time period

Where, I = Moment of inertia of bar magnet


M = mass of the magnet


B = Magnetic Field


Bar magnet is oscillating in Uniform Magnetic Field


Moment of Inertia


Initial time period


When the bar magnet is cut into two equal pieces each of mass () and length ()



Hence



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