Question

Two different magnets are tied together and allowed
to vibrate in a horizontal plane. When their like poles
are joined, time period of oscillation is 5 s and with
unlike poles joined, time period of oscillation is 15 S.
The ratio of their magnetic moments is

Answer 1

Answer:

The ratio of their magnetic moments is 5 : 4.

Explanation:

We have 2 different magnets which are tied together and is allowed to vibrate in a horizontal plane.

Let the time period of oscillation when the like poles are joined be “T1” and the time period of oscillation when unlike poles are joined be “T2” and let their magnetic moments be “M1” and “M2” respectively

Here,  

T1 = 5 s

T2 = 15 s

We know that according to the sum and difference position method of vibration of a magnet, the ratio of the magnetic moments is given by

$\frac{M1}{M2}$ = $\frac{T2^2 + T1^2}{T2^2 - T1^2}$

Or, $\frac{M1}{M2}$

= $\frac{15^2 + 5^2}{15^2 - 5^2}$

= $\frac{225 + 25}{225 - 25}$

= $\frac{250}{200}$

= $\frac{5}{4}$

Hence, M1 : M2 :: 5 : 4.