Question

Two magnets are placed one above the other with like poles together the time period of this combination is $10$ seconds. Now they are placed one above the other with unlike poles together the time period of this combination is $20$ second in the same field.The ratio of magnetic moments is

• A. $3:1$
• B. $5:1$
• C. $5:3$
• D. $3:5$

Answer 1

The correct option is C $5:3$

Let magnetic dipole moment of magnets are $M_1$ and $M_2$ and their combined moment of inertia is $I$.

Like poles together

$M_{net}=M_1+M_2$

$T=2\pi \sqrt{\frac{I}{MB}}$

$10=2\pi \sqrt{\frac{I}{(M_1+M_2)B}}$ (1)

Unlike poles together

$M_{net}=|M_1-M_2|$

$20=2\pi \sqrt{\frac{I}{|M_1+M_2|B}}$ (2)

$\therefore \frac{10}{20}=\sqrt{\frac{|M_1-M_2|}{M_1+M_2}}$

or, $\frac{1}{4}=\frac{|M_1-M_2|}{M_1+M_2}$

Let $M_1>M_2$

Then, $\frac{1+4}{1-4}=\frac{M_1-M_2+M_1+M_2}{M_1-M_2-M_1-M_2}$

$\frac{5}{-3}=\frac{M_1}{-M_2}$

or, $\frac{M_1}{M_2}=\frac{5}{3}$