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

Explanation:

For oscillating magnets, use the formula for time period.

Step 1:

Time period of original magnet

Time period for oscillating magnet is:

T=2π  

MB I

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

Moment of Inertia,  I=  12 M  ′ L  2

When a magnet is divided into two equal halves, its mass and length are both reduced by a factor of two. S new moment of inertia is 1/8th that of the initial moment. Magnetic mornent also equals pole strength x length. The pole's strength is unaltered, but its length has been reduced by half. As a result, the new magnetic moment is equal to one-half of the original magnetic moment. T=2IMB Now, = 2I/8M2B=T4=T2,TT=12 T=2IMB T=2IMB T=2IMB T=2IMB T=2IMB T=2IMB T=2IMB T=2IMB