Q137 / 160 · TS EAMCET 2010 · Physics

The frequncy of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 \mathrm{~Hz}$ when like poles are tied and it is $2 \mathrm{~Hz}$ when the unlike poles are tied together, then the ratio $M_1: M_2$ is

  • A
    $4: 5$
  • Correct answer
    B
    $5: 4$
  • C
    $1: 3$
  • D
    $3: 1$

Solution

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, $T_1=\frac{1}{n_1}=\frac{1}{6} \mathrm{~s}$ $T_2=\frac{1}{n_2}=\frac{1}{2} \mathrm{~s}$ $\frac{M_1}{M_2}=\frac{\frac{1}{4}+\frac{1}{36}}{\frac{1}{4}-\frac{1}{36}}+\frac{\frac{9+1}{36}}{\frac{9-1}{36}}$ $=\frac{10}{8}=\frac{5}{4}$ $M_1: M_2=5: 4$

Hence, the correct answer is option: 'B'.

More Magnetic Properties of Matter Questions