Question

A thin bar magnet is cut into two equal parts.the ratio of moment of inertia to the magnetic moment of each part will become?(as compare to original magnet)
solution please.
options-1) 1/2
2)1/4
3)1/8
4)1

Answer 1

answer : option (2) 1/4

explanation : let initial magnetic moment is M.

after cutting thin bar magnet into two equal parts, magnetic moment of each part of bar magnet is M/2.

I.e., $M_{final}$ = M/2

we know, moment of inertia , I ∝ ml²

hence , after cutting thin bar magnet into two equal parts, mass of each part is (m/2) and length of each part is (l/2).

so, I1/I2 = (ml²)/{m/2(l/2)²} = 1/8 .

i.e., $I_{final}$ = I/8

now, ratio of Moment of inertia to magnetic moment of each part = (I/8)/(M/2) = (1/4) × I/M

= 1/4 × ratio of moment of inertia of initial thin bar magnet.

hence, option (2) is correct choice.

Answer 2

Answer:

Magnetic moment final equal to M/2 beacuse its length is halved.

I=mass×l^2

Now,mass of each piece is halved so, it is m/2 and lengthis also l/2

So,I=m/2×l^2/4=ml^2/8

Now,I/ M = ml^2/8×2/M=1/4ml^2/M

So ,answer is 1/4