Q. The time period of a thin bar magnet in earth's magnetic field is T . If the magnet is cut into two equal parts perpendicular to its lenght the time period of the each part in the same will be ..??????????????plz ans it soon..:)
The time period of an oscillating magnet is given as
T = 2π (I / MB)1/2
here
I is the moment of inertia = (1/2)ml2
M is the magnetic moment
B is the magnetic field strength
now, as the magnet is cut in to two equal parts, the new length becomes l' = l/2 and thus, the magnetic moment will also be halved. So, the new time period will be
T' = 2π (I' / M'B)1/2
or
T' = 2π ((I/4)/[(M/2)*B])
now, T'/T = 2π (I' / M'B)1/2 / 2π (I / MB)1/2
or
T'/T = 1/2
or
the new time period will be
T' = 2T