Q104 / 120 · VITEEE 2009 · Physics

Two bar magnets A and B are placed one over the other and are allowed to vibrate in a vibration magnetometer. They make 20 oscillations per minute when the similar poles of A and B are on the same side, while they make 15 oscillations per minute when their opposite poles lie on the same side. If $M_{A}$ and $M_{B}$ are the magnetic moments of $A$ and $B$ and if $M_{A}>M_{B}$, the ratio of $\mathrm{M}_{\mathrm{A}}$ and $\mathrm{M}_{\mathrm{B}}$ is

  • A
    $4: 3$
  • Correct answer
    B
    $25: 7$
  • C
    $7: 5$
  • D
    $25: 16$

Solution

Ratio of magnetic moments $$ \begin{aligned} \frac{M_{A}}{M_{B}} &=\frac{T_{d}^{2}+T_{s}^{2}}{T_{d}^{2}-T_{s}^{2}}=\frac{v_{s}^{2}+v_{d}^{2}}{v_{s}^{2}-v_{d}^{2}} \\ &=\frac{\left(\frac{1}{20}\right)^{2}+\left(\frac{1}{15}\right)^{2}}{\left(\frac{1}{15}\right)^{2}-\left(\frac{1}{20}\right)^{2}}=\frac{400+225}{400-225} \\ M_{A}: & M_{B}=25: 7 \end{aligned} $$

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

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