Question

A thin rectangular magnet suspended freely has a period of oscillation equal to t. Now it is broken into two equal halves(each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is t', the ratio t'/t is :-

Answer 1

ANSWER - 1/2

EXPLAINATION -

Use formula for time period for oscillating magnet

Step 1: Time period of original magnet

Time period for oscillating magnet is:

T=2πMBI

where, Magnetic Moment M=xl ( x is the pole strength and l is length)

Moment of Inertia, I=12M′L2

Step 2: Time period of one part of magnet

When the magnet is broken in two equal parts, the new magnetic dipole moment is

Mnew = 2x×l = 2M

=> Inew=12(M′/2)×(L/2)2=12×8M′L2

=8I

∴ New Time Period is

Tnew = 2π MnewBInew

Step 3: Ratio of Time period in both cases

Taking the ratio of Tnew and T we get :

TTnew=MnewInew×IM

=IInew×MnewM

=81×12 = 21