A thin bar magnet oscillating in a uniform magnetic field has a time period of 4 s . The magnet is then cut into two equal halves perpendicular to its length. If one of these halves is suspended to oscillate in the same magnetic field, its new time period will be:

Step-by-step solution

Let the initial mass, length, moment of inertia, and magnetic moment of the bar magnet be m , L , I , and M respectively. The initial time period is T = 2 I MB = 4 s When the magnet is cut into two equal halves perpendicular to its length, the mass of each half becomes m' = m 2 and the length becomes L' = L 2 . The new moment of inertia for one half is: I' = m'(L')^2 12 = ( m 2 ) ( L 2 )^2 12 = 1 8 ( mL^2 12 ) = I 8 The pole strength remains unchanged, but the magnetic length is halved. Thus, the new magnetic momen