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5.Magnetism and Matter
hard
Magnets $A$ and $B$ are geometrically similar but the magnetic moment of $A$ is twice that of $B$. If $T_1 $ and $T_2$ be the time periods of the oscillation when their like poles and unlike poles are kept together respectively, then $\frac{{{T_1}}}{{{T_2}}}$will be
A
$\frac{1}{3}$
B
$\frac{1}{2}$
C
$\frac{1}{{\sqrt 3 }}$
D
$\sqrt 3 $
Solution
(c)${T_{Sum}} = 2\pi \sqrt {\frac{{({I_1} + {I_2})}}{{({M_1} + {M_2}){B_H}}}} $
${T_{diff}} = 2\pi \sqrt {\frac{{{I_1} + {I_2}}}{{({M_1} – {M_2}){B_H}}}} $
$ \Rightarrow \frac{{{T_s}}}{{{T_d}}} = \frac{{{T_1}}}{{{T_2}}} = \sqrt {\frac{{{M_1} – {M_2}}}{{{M_1} + {M_2}}}} = \sqrt {\frac{{2M – M}}{{2M + M}}} = \frac{1}{{\sqrt 3 }}$
Standard 12
Physics
