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5.Magnetism and Matter
hard
The magnet of a vibration magnetometer is heated so as to reduce its magnetic moment by $19\%$. By doing this the periodic time of the magnetometer will
A
Increase by $19\%$
B
Decrease by $ 19\%$
C
Increase by $ 11\%$
D
Decrease by $21\%$
Solution
(c)$T = 2\pi \sqrt {\frac{I}{{M{B_H}}}} \Rightarrow T \propto \frac{1}{{\sqrt M }} \Rightarrow \frac{{{T_1}}}{{{T_2}}} = \sqrt {\frac{{{M_2}}}{{{M_1}}}} $
If $M_1 =100$ than $ M_2 (100 -19) = 81$
So $\frac{{{T_1}}}{{{T_2}}} = \sqrt {\frac{{81}}{{100}}} = \frac{9}{{10}} \Rightarrow {T_2} = \frac{{10}}{9}{T_1} = 1.11\,{T_1}$
$ \Rightarrow $Time period increases by $11\%$
Standard 12
Physics
