Question

A thin bar magnet is cut into two equal parts as shown in the figure. The ration of moment of inertia magnetic moment of each part will become (as compare to original magnet)

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{8}$
• D. $1$

Answer 1

The correct option is B $\frac{1}{4}$

From the given data,

Initial moment of inertia $=m{l}^2$

Initial magnetic moment $=polestrength\times 2l$

Their ratios is $=\frac{ml}{2\left(polestrength\right)}.........\left(1\right)$

After cutting the magnet, pole strength remains the same.

Final moment of inertia $=\frac{m}{2}{\left(\frac{l}{2}\right)}^2=\frac{m}{8}$

Pole strength

$=polestrength\times 2\left(\frac{l}{2}\right)$

$=polestrength\times l$

Their ratios $=\frac{ml}{8\left(polestrength\right)}............\left(2\right)$

Ratios of magnetic moment of two parts is

$=\frac{\frac{ml}{8\left(polestrength\right)}}{\frac{ml}{2\left(polestrength\right)}}$

$=\frac{1}{4}$