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5.Magnetism and Matter
hard
Two magnets are held together in a vibration magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together, $12$ oscillations per minute are made but for unlike poles together only $4$ oscillations per minute are executed. The ratio of their magnetic moments is
A
$3:1$
B
$1:3$
C
$3:5$
D
$5:4$
Solution
(d)In the sum and difference method of vibration magnetometer
$\frac{{{M_1}}}{{{M_2}}} = \frac{{T_2^2 + T_1^2}}{{T_2^2 – T_1^2}}$
Here ${T_1} = \frac{1}{{{n_1}}} = \frac{{60}}{{12}} = 5\sec .\;{T_2} = \frac{1}{{{n_2}}} = \frac{{60}}{4} = 15\sec $
$\therefore \frac{{{M_1}}}{{{M_2}}} = \frac{{{{15}^2} + {5^2}}}{{{{15}^2} – {5^2}}} = \frac{{225 + 25}}{{225 – 25}} = \frac{5}{4}$
Standard 12
Physics
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